UNIVERSITY OF CALIFORNIA,
UNIVERSITY OF CALIFORNIA
DEPARTMENT OF PHYSICS
^cessions No. & f Z Book m _/
J. S. AMES, PH.D.
PROFESSOR OF PHYSICS IN JOHNS HOPKINS UNIVERSITY
THE LAWS OF RADIATION AND ABSORPTION
RADIATION AND ABSORPTION
MEMOIRS BY PROVOST, STEWART, KIRCHHOFF,
AND KIRCHHOFF AND BUNSEN.
TRANSLATED AND EDITED BY
D. B. BRACE, PH.D.
PROFESSOR OF PHYSICS IN THE UNIVERSITY OF NEBRASKA.
NEW YORK : CINCINNATI -: CHICAGO
AMEEICAN BOOK COMPANY
COPYEIGHT, 1901, BY
AMERICAN BOOK COMPANY.
Entered at Stationers'' Hall, London.
Radiation and Absorption.
W. P. i
THE attempt of Prevost to explain the experiments of Pictet,
of the apparent concentration of cold at the focus of a mirror,
without attributing the quality of radiation to cold, as assumed
by Pictet, lead him to the enunciation of the very important
principle which he called the movable equilibrium of heat, now
designated as the theory of exchanges. Prevost, who was a dis-
ciple of le Sage, and who had issued, with many additions, his
memoirs, assumed, in addition to a corpuscular fluid caloric, a
free corpuscular radiant caloric, the equal interchange of which
between neighboring free spaces, constituted heat equilibrium.
Any interference with this equilibrium will be reestablished by
the inequalities of the exchanges. On this principle he was able
to explain the apparent concentration of cold and also to show
the inadmissibility of cold as an agent susceptible of radiation.
He was careful, however, to fortify his principle by showing that
the same results would follow on the then distrusted hypothesis
of undulatory exchanges, which has been adopted by his suc-
cessors. Later experimenters, particularly Leslie and De la
Provastaye and Desains, confirmed the theory and also showed
in many instances quantitative relations between radiation and
absorption. But the most important advance was made by Bal-
four Stewart in establishing, not only a quantitative relation,
but also a qualitative or selective one. By the introduction of
his ingenious idea of an impervious radiating inclosure he
demonstrated the equality between the emissive and the absorp-
tive power of any wave length. We owe to Kirchhoff, however,
the first rigorous proof of the celebrated law (usually designated
on the Continent as KirchhofFs law) of the emission and absorp-
tion of light and heat, and the application of the same by both
Kirchhoff and Bunsen to Spectrum Analysis. The radiation
of solids and liquids and gases follows the law exactly when the
conditions upon which he founded it are rigorously fulfilled,
namely, the complete transformation from one to the other of
radiant energy and their intrinsic heat. "We now know that
most radiations from gases are not exclusively thermal, but that
the substances, cited by Kirchhoff and Bunsen, also give off so
called chemical and electrical and fluorescent radiations which
Kirchhoff excluded in the proof of his law. In fact none of the
gases giving line spectra at temperatures heretofore used do so
by simple thermal radiation, but essentially by luminescent
actions (chemical, electrical, and photogenic), so that we cannot,
in general, apply the law of Kirchhoff of the proportionality
between radiation and absorption to either terrestrial or celes-
tial substances. In these cases the principle of resonance usually
holds, since in luminescence the radiation of line spectra is
accompanied by selective absorption of the same spectral lines,
so that the law may be used qualitatively, which is in ftict the
way Kirchhoff and Bunsen actually attempted to confirm it.
The formulation of the complete law for radiations of a Hack
body is only given in part by Kirchhoff. The formula of Wien,
and more particularly the most recent one of Planck, deduced
on theoretical grounds, approximates closely the latest observa-
tions on a black body at different temperatures and over differ-
ent wave lengths.
D. B. BRACE.
University of Nebraska.
Preface ' . v
On the Equilibrium of Heat. Pierre Prevost .... 1
Treatise on Radiant Heat (Selections). Pierre Prevost . . 15
Biographical Sketch of Prevost 20
An account of some Experiments on Radiant Heat, involv-
ing an extension of Prevost's Theory of Exchanges.
By Balfour Stewart 21
Researches on Radiant Heat. Second Series. By Balfour-
Stewart . . 51
Biographical Sketch of Stewart. ... . . 72
On the Relation between the Emissive and the Absorptive
Power of Bodies for Heat and Light. By G. R. Kirch-
Biographical Sketch of Kirchhoff ... . 97
Chemical Analysis by Spectral Observations by G. Kirch- 126
hoff and R. Bunsen ... .... 99
Biographical Sketch of Bunsen . . 126
Index , ..... 129
MEMOIR ON THE EQUILIBRIUM OF HEAT.
Journal de Physique, vol. 38, pp. 314-322. Paris, 1791.
Outline of the Proposed Discussion 3
Theory of the Equilibrium of Heat ..... 4
Rupture of the Equilibrium between two Portions of Space 6
Phenomenon of Reflection of Cold . . . . . 7
Exclusion of an Independent Explanation . . . . 9
Supplementary Remarks on Radiant Heat . . .11
Discussion of /Several Discrete Fluids . " . . . . 12
MEMOIR ON THE EQUILIBRIUM OF HEAT.
BY PIERRE PREVOST.
I PROPOSE to analyse and fix with precision the sense of the
word equilibrium applied to such a fluid as heat. This idea is
not exactly defined in the theories which leave questions rela-
tive to the nature of this element undecided. If there is any
doubt that heat is material, if there is no explanation concern-
ing the contiguity or the noncontiguity of molecules of heat,
concerning their mobility or their immobility, the kind of
motion, vibratory or translatory, which is attributed to them, *
it is impossible to arrive at exact and complete ideas of their
equilibrium. It results from this that every phenomenon which
depends, not upon any equilibrium whatever but upon a spe-
cific kind of equilibrium, remains entirely unexplained. And
as the imagination determines to some extent, notwithstanding,
that which reason wishes to leave undetermined, the true
causes are lost sight of, and vain hypotheses are arbitrarily
preferred because they are suitable in certain respects and fav-
orable to first appearances.
I will not waste time in discussing the different natures
assigned to heat by various physicists. The true constitution"
of this fluid is connected with the theory of discrete fluids, now
known, although it has not been published by its author. For
its development and proof I refer to what M. DeLuc has said
of it both in his " Idees sur la meteorologie" and in his letters
published successively in this Journal: also what I have said of
it myself in my essay upon I'origine des forces magnetiques.
Assuming then the principles of this theory, I shall merely recall
them, and use them to establish true ideas on the equilibrium
I shall afterwards make the application of this theory of the
equilibrium of heat to a very remarkable phenomenon which I
consider inexplicable without it. This is the phenomenon of
the reflection of cold. It has been observed by M. Pictet, who
has described it in detail in his essai sur le feu. This learned
scientist, with whom I have old and valued bonds of friendship,
does not at all disapprove of the discussion which I am under-
taking although it tends to indicate some inadequacy in the
explanation which he, himself, has given to this phenomenon.
It will be seen elsewhere by what I shall say of it, that a com-
plete explanation, such as the theory of M. le Sage furnished,
does not enter into the plan which M. Pictet has proposed. I
will discuss this phenomenon then, very freely. I shall show that
it explains itself without any effort, by the true theory of dis-
crete fluids. I shall also prove that it is not explained at all by
the imperfect theories to which physicists commonly limit
themselves. I shall close this memoir with two remarks which
have some connection with this subject, without being directly
related to it.
THEORY OF THE EQUILIBRIUM OF HEAT.
Heat is a discrete fluid. Its elasticity consists in its expau-
^ sive force. And this is the effect of the movement of its
particles. This movement is caused by the impulse of a much
more subtile fluid whose effect upon its particles is determined
to a certain extent by their form. It is so swift that when heat
NO is freed its translation from one place to another appears in-
stantaneous. It is also sensibly rectilinear, so that perfectly
free heat partakes, as far as the movement of its particles is
concerned, of all the properties of light, at least so far as our
senses can determine in the limited experiments which have
thus far been performed.
A discrete fluid whose particles radiate like those of light,
may be confined by barriers, but may not be confined by an-
other radiant fluid nor, in consequence, by itself. For it is
necessary to conceive of all these fluids as very rare, as having
many more void intervals than full ones in the space which
they occupy. Light does not stop the passage of light. If this
solar emanation is so dense that two luminous currents cannot
cross each other without being interrupted, the innumerable
crossings and reflections which they experience will destroy
entirely its rectilinear direction, and light will lose to our eyes
RADIATION AND A B S R P T 1 N .
all its properties which depend upon this direction. What is
true of this fluid is true of all radiant fluids. Radiant heat
passes through heat, which upon the earth is present in all
places, and since it produces no sensible perturbation, it is nec-
essary that these particles should be separated by intervals great
relatively to their diameters. It is certain that free radiant
heat is a very rare fluid, the particles of which almost never
collide with one another and do not disturb sensibly their mu-
In conforming to physical hypotheses, one says ordinarily
that heat is coercible by itself : that two contiguous portions of
heat have a mutual relation when their temperatures are equal
(or as M. Volta has said, when their tensions are the same).
These expressions are exact, only in so far as they define an ap-
pearance. In reality the heat of any portion cannot arrest that
of another. These two heats give each other mutually free
passage. It would then be wrong for one to conclude from
these expressions that two portions of contiguous heat restrain
each other mutually, as two bent springs stayed against
one another, or as two masses of hair which repel each other
by their elasticity.
But in what does the equilibrium of these two portions of
contiguous heat consist ? In order to answer this question
clearly, I will suppose the two portions to be enclosed in an
empty space, terminated on all sides by impenetrable walls.
One may represent two cubes applied by one of their faces,
forming in consequence a rectangular parallelepiped perfectly
hollow, of which the six faces are of the same matter, absolutely
solid and without pores. The two portions which I consider
are, in this example, the two applied cubes. The heat occupy-
ing the interior of this space moves freely there, and as-
suredly one can see no reason why it should pass with less
facility across the boundary of the two portions than across
every other section of this space. There are then continual ex-
changes from one portion to another, and one can affirm (in
consideration of the number of particles and their continual
motion) that at each observable instant the state and quantity
of the heat in each portion are constant. There is then no
ceasing of the different particles, which are found at any one
MEM OIKS ON
place, but their number and their meau distance in each
portion are constant. Concerning their speed, as it is in the
same free fluid (consider the constant nature of the cause
which produces and renews it continually), it is clear that it
does not change : and I shall leave it out of the question, since
at the present moment I consider only free radiant heat.
At all times that both portions of the space are found in the
circumstances which I have just described, the heat between
them is in a state of equilibrium. This signifies that the
phenomena which manifest their existence remain the same :
that if these phenomena change in the same manner and in the
same quantity in the two portions, the equilibrium in question
will not be disturbed. This would occur if one should remove
from the total space, which we are considering, a certain
aliquot part of all the heat found there, or indeed if this
aliquot part should be added. The identity of the phenomena
which implies the equilibrium of heat between these two por-
tions of space is a relative identity, which, as one can see, may
exist whatever may be the difference or the absolute in-
Let us now suppose that into one of the two portions of space
(which I will represent constantly by the two adjoining cubes)
one passes suddenly some new heat ; for example, one tenth of
all that which is contained in this portion. This heat, in-
stantly placed in motion, spreads immediately throughout all
the space where it can penetrate freely. Thus the exchanges
between the two portions would be unequal. One would send to
the other eleven particles, while the latter would return only
ten. This state causes a rupture of the equilibrium between
the two portions.
By reason of the unequal exchanges one may conceive that
the equality would be reestablished. Thus the rupture of the
equilibrium restores very quickly the equilibrium between two
portions of free heat. 1
1 Suppose that the densities of the heat in our two cubes are as the
numbers 1 and 2 (i. e., that one is twice as hot as the other) : suppose
further that in one second there passes from the one cube to the other a
number of igneous particles which on the whole are as 1 to 10 (so that
during this short time there is exchanged one tenth of all the heat).
RADIATION AND ABSORPTION.
Absolute equilibrium of free heat is the state of this fluid in
a portion of space which receives as much as it allows to
Relative equilibrium of free heat is the state of this fluid in
two portions oi' space which receive from each other equal
quantities of heat, and which are, moreover, in absolute equilib-
rium, or experience changes precisely equal.
The heat of several portions of space at the same temperature
and near each other is at once in the two kinds of equilibrium.
If one should change the temperature of all the space at the
same time, it would destroy the absolute equilibrium, but not
the relative equilibrium. Should the temperature of one or
of several portions be altered without affecting all, each kind
of equilibrium would be destroyed.
If the cause which throws out or which absorbs the heat of
any portion is an instantaneous cause, after the action of this
cause the relative equilibrium reestablishes itself incessantly
by means of unequal exchanges. And after this reestablish-
ment the absolute equilibrium remains destroyed, that is to
say, the temperature of the place is changed.
If, on the contrary, the cause is permanent, that is to say, if
there is opened in any one of the portions of this space a source
or a sink which gives out or which absorbs heat incessantly, rela-
tive equilibrium tends to establish itself, but does not reestablish
itself entirely during the action of the cause, and absolute
equilibrium is constantly destroyed.
APPLICATION OF THE PRECEDING THEORY TO THE
PHENOMENON OF REFLECTION OF COLD.
Let us represent two spherical concave mirrors opposite to
each other on their axes, and let us suppose placed at their foci
After seven seconds the ratio of the densities of the heat in the two
cubes will be as 5 to 6. After fourteen seconds, these densities will be
as 28 to 29, i. e., very nearly equality : the equilibrium will appear
I take this result from a calculation of M. le Sage thirty years since in
the case of discrete fluids different from heat.
two bodies precisely equal and similar and of the same sub-
stance, which JL will call the two focal bodies.
To simplify this I will suppose, (1) that all the space where
the apparatus is immersed is absolutely cold and receives heat
only from part of the two focal bodies, (2) that these are hot
and give out radiant heat continuously, (3) that the mirrors re-
flect the heat but do not absorb it.
With these conditions, it is clear that the heat thrown out by
either one of the two focal bodies radiates on all sides. But I
shall consider only the part which strikes the mirror of which
it is the focus.
This heat is reflected parallel to the axis. Striking the op-
posite mirror in this direction, it is reflected to the focus of
this second mirror and enters as a consequence the body which
occupies this focus. Similarly inversely, the heat thrown out
by this latter against its mirror enters after two reflections the
body which occupies the focus of the first mirror.
Let us suppose, first, the two focal bodies are at the same
temperature, or each one sending out in equal intervals of time
an equal quantity of radiant heat to its own mirror. The
relative equilibrium of heat between the two focal bodies will
not be disturbed by this operation, ; for each of them will re-
ceive from the other exactly what it gives up to it. Radiation
will exactly compensate absorption.
Now let us change, to a greater or less degree, the tempera-
ture of one of the two focal bodies ; the exchanges made between
them by means of double reflection will cease to be equal : the
relative equilibrium will be destroyed. It will tend then to re-
establish itself, and the temperature of these two bodies will ap-
proach each other. If additional heat should be thrown upon
the first body, for example, a tenth of all that which it has, the
second body will make advantageous exchanges with it. For
ten particles transmitted by reflection, it will receive eleven by
the same means : in this way its heat will be augmented.
If one should withdraw heat from the first body, for example
a tenth, the- second body will make exchanges at a loss, receiving
nine against ten by means of the mirror. It will be cooled.
Such is the result of the theory conforming exactly to that
of the ingenious experiments of M. Pictet, in spite of all the
RADIATION AND ABSORPTION.
conditions which 1 have made, since these conditions influence
only the quantity of cold or of heat produced by reflection,
and not the nature of these actions. It is known that this
physicist has observed heat and cold equally reflected in his ap-
paratus, which is such as I have just described. He has not
hesitated to explain the reflection of cold just as that of heat in
a reciprocal sense : but being limited (conformably to his
representation) to explanations drawn at once from experiment,
and it not being his purpose, in the important work which he
has published, to treat of the constitution of discrete fluids, he
has not been able to enter into the details which I have just
given. It has resulted from this that the view to which he has
come touching the cause of the reflection of cold, founded upon
these notions of equilibrium, inapplicable to discrete fluids, is
insufficient for the theory, however true as to appearances.
It is certain that when one produces cold at the focus of one
of the mirrors, the heat of the thermometer placed at the op-
posite focus follows the course which M. Pictet traces for it.
And this course is what I have just described. But what it is
that causes the excess heat of the thermometer to take this
course, this physicist has not shown me, because he has not
been called upon to consider heat according to its natural con-
stitution. Now if one holds to the ideas of tension, of stress,
in a word, of unvariable equilibrium, he finds that the progress
of the phenomenon of heat in the experiment of the reflection
of cold remains absolutely inexplicable. I shall now show, (1)
that in this hypothesis of unvarying equilibrium no heat ought
to pass from the thermometer to its mirror, (2) that if any does
pass, this heat should not converge to the focus of the other
EXCLUSION OF THE INDEPENDENT EXPLANATION
OF THIS THEORY.
(I) At the instant when one places a cold body, such as glass,
at the focus of one of the mirrors, the heat of all the neighbor-
ing bodies passes into it. This cause acts according to the law
of the inverse square of the distance, when we suppose the
bodies to be of the same nature, as we do in this instance.
The mirrors employed in the experiment of the reflection of
cold were placed ten and one half feet apart. Their curvature
was that of a sphere with a radius of nine inches : so that their
foci were about four and one half inches from their surface,
measured on the axis.
If, then, we consider only the apparatus without taking into
account the supports, or the air or the surrounding and neigh-
boring bodies, it is clear that the mirror whose focus is occu-
pied by the glass, being twenty-eight times nearer this cold
body than the other mirror, ought to send out to it seven him-,
dred and eighty-four times as much heat in the same time.
Further, the thermometer placed at the focus of this other
mirror being nearer the glass than its mirror in the ratio of 26
to 27, ought to set free more heat than a portion of the mirror
equal to its bulb in the double inverse ratio (at least for the
part of the mirror which lies at the origin of the axis). This
ratio is that of 729 to 676, or of about 13 to 12 ; so that,
through the direct influence of the glass, the thermometer loses
about a thirteenth more of its heat than if it formed a part of
the mirror, at the focus of which it is placed. When the cool-
ing of the first mirror becomes sensibly equal to the second, the
thermometer being less distant than the former, is also more
affected by the latter in the double inverse ratio of 27 to 28 ;
that is to say, in the ratio of 784 to 729, or of about 14 to 13.
Thus the thermometer is cooled more than its mirror, either
directly by the glass, or indirectly by the mirror whose focus
this glass occupies. Heat here then is under less tension than
in the mirror. Consequently it cannot pass from the thermome-
ter to the mirror, nor in consequence, radiate from there to the
opposite mirror next the glass. This progress of the phenomena
in a system in unvarying equilibrium is contrary to the effect
which the cause should occasion. And it is still more inexpli-
cable when we consider the supports of the apparatus and all
the surrounding bodies which send heat into the glass, and
constantly draw out that of the thermometer, as well as of the
opposite mirror: effects independent of reflection and of the
particular position of the foci.
RADIATION AND ABSORPTION.
(II). To which it is necessary to add, in reconciling the
same (which is demonstrated false in the hypothesis I have dis-
cussed), that the heat of the thermometer passes in part into
its mirror; as there is carried over only what replaces that which
escapes, this heat would not be reflected, but absorbed. Now,
all the heat which one of the mirrors sends out to the other,
aside from that by reflection to the focus, being an irregular
radiation, would not converge at the focus of the other mirror.
THUS the foci would not be more characteristic than two other
points, taken at random between the mirrors, for repeating the
experiment of reflection of cold, which is absolutely contrary
to the actual observation.
It is apparent, then, that if we refuse to consider heat
according to its true constitution as a discrete fluid, whose
particles are in motion, and if in consequence we do not arrive
at ideas which I have given of the equilibrium of radiant free
heat, it is impossible to give any satisfactory explanation (com-
patible moreover with the principles of sound physics), of this
beautiful and remarkable phenomenon of the reflection of cold.
The fact is established by an excellent observer, who has very
clearly recognized the progress of the phenomena of heat. The
discovery of the cause is due to the author of the true theory of
(1). Radiant heat is only a part of the heat that escapes from
a hot body. Let us suppose that in the preceding experiment
the two foci of the mirrors communicate by a metallic bar, termi-
nated at both ends by these foci: if we place at one end of the
extremities of this bar an exhaustless source of heat (a red-hot
iron, a blast-lamp flame, the focus of a powerful lens): immedi-
ately the radiant heat, following the course indicated above,
will warm the other extremity of the bar by the double reflec-
tion. At the same time the non-radiant heat, creeping gradu-
ally into the contiguous parts of the bar, will slowly heat it and
will finally come to the points most distant from the source.
The air being a discrete fluid much more dense 1 than heat,
arrests and intercepts the particles of the latter. But being
much more rare than the metal, it allows a portion of it to pass,
which produces the phenomena of radiant heat. Light, much
more rare and subtle than heat, is transmitted in much greater
proportion by this same air, the opacity of which is so incon-
siderable that it becomes sensible only in very great masses. 2
The transparency or the quantity of fluid transmitted through
another fluid, depends upon the rarity and the subtlety of the
particles of both fluids. I do not speak here of the affinities
and capacities of different bodies for heat. I speak only of the
mechanical interception of this fluid by its solid parts. This
interception is sufficient only to produce these two kinds of
heat or of cold, radiant heat, and nonradiant heat.
Entangled, further, in the small cavities or in the interstices
of solid particles, the heat may or may not recover all the veloc-
ity which properly belongs to it, according as these cavities or
interstices are or are not sufficiently spacious. When it recov-
ers only a portion of its velocity, it becomes in part insensible
or latent. When it can recover only a very little of it or none
at all, it yields to the affinities of the particles which surround
it and combines in a thousand ways.
(2). Heat is not the only fluid of its kind. Several discrete
fluids are known, radiant and nonradiant. 3 We often have
occasion to consider these fluids in the state of equilibrium.
The determination of the true sense of this word ought then to
be of much importance, independently of the theory of heat.
1 The density which I attribute to the air in this instance, consists
chiefly in the proximity of its molecules; for a discrete fluid maybe
composed of very dense particles, but with large spaces between them :
so that it could be more permeable than heat, although more dense.
2 Notice the remarks of M. de Saussure, upon the transparency of
the air, in his memoirs upon light. Academ. de Turin, 1790.
8 In the electrical phenomena, there are radiations of the correspond-
ing fluid. In magnetic phenomena neither of the two magnetic fluids is
RADIATION AND ABSORPTION.
If these remarks and the preceding discussion offer any
useful views, if they tend to throw light upon an important
class of phenomena, if they suggest any clear ideas upon the
method of motion of invisible and subtle fluids which manifest
their existence by such diverse appearances : finally, if these
conceptions naturally connect themselves with other theories,
either already proven, or rendered probable, concerning the
various effects of these subtle fluids (such, as the phenomena of
evaporation, of electricity and of magnetism), is it not the
requital of investigating the general theory upon which all
these special explanations depend ? This theory (I refer to
that of M. le Sage of Geneva, upon the nature of discrete
fluids) merits the further attention of physicists, since it depends,
itself, upon another principle, more general, which has also as
a proof of its reliability, the clear and satisfactory explanation
of very striking and very general phenomena, absolutely in-
explicable without it.
ON RADIANT HEAT.
Questions Relative to the Nature of Caloric . _ . . 17
Resume of Principles and Conclusions. . . . . 19
QUESTIONS RELATIVE TO THE NATURE
CHAPTER IV. PP. 6 10.
THE word caloric (heat) has been originated to explain the
cause of heat, with the formally expressed intention of being
non-committal as to its nature.
It is desirable to leave it indefinite as to whether heat may be
produced by a specific fluid, or, merely, be a movement
impressed upon the molecules of a body, without the introduc-
tion of any fluid.
Many noted physicists believe there is no specific fluid to
which this word caloric is applicable. They believe that heat
is produced by internal movements of the molecules of a body.
More often, however, physicists have recourse to a vibrating
ether or to the air, or to some other medium propagating waves
to which they attribute the phenomena of heat.
Others believe that caloric is a specific fluid, which penetrates
the body and produces all the appearances of this kind.
Among the latter, many believe that caloric and light are
identical. Others are of a contrary opinion.
Some look upon caloric as simple ; a smaller number regard it
as a compound fluid. Mr. J. A. DeLuc believes that caloricis, a
kind of vapor composed of ponderable matter held in a state of
suspension by light. This conception throws some light upon
many phenomena and merits serious consideration. Meanwhile,
pressed to arrive at the chief object which I have in view, I
will refrain from all discussion as to the composition of caloric.
I have no desire to repeat here and weigh the general
arguments stated on the one side and on the other for sus-
taining the various views which I have just outlined. I will
limit myself to a very few remarks on this subject.
As stated below I propose to consider caloric as a specific
fluid. I will represent the radiations of this fluid as an emission
RADIATION AND ABSOKPTION.
and never as an undulation. I believe this conception and this
representation to be more conformable than any other to the
nature of things and founded upon the soundest principles of
general physics. But if those who believe otherwise substitute
waves for an emission they may be able, perhaps, to adapt to
their opinion the explanations which I give for phenomena of
this crass. It is no desire of mine that they should attempt it,
because I am persuaded that this would be translating a
language clear and natural into a language obscure and artificial.
But I make this statement to make clear the kind of work
which I have undertaken. I do not contest any system. I do
not refute any explanation. It is my aim, in limiting myself in
my subject, to explain in my own way what seems to me to ad-
mit of clear explanation, and to indicate the phenomena of
which the explanation remains imperfect. If each one who
has an opinion upon the theory of caloric will give a concise ex-
position of his ideas on the subject, and will show how the facts
may be coordinated by means of these conceptions : physicists
can see at a glance which theory is most satisfactory, or if all
should be rejected.
RESUME OF THE PRINCIPLES EXPOUNDED AND OF THE PRINCI-
PAL CONCLUSIONS WHICH HAVE BEEN DEDUCED
SECTION IX. pp. 258261.
HEAT is a discrete fluid; each element of heat follows con-
stantly the same straight line, as long as no obstacle arrests it.
Every point of a hot space is constantly traversed throughout
by streams of heat.
If we admit this constitution of heat, the following conclu-
sions are inevitable.
The first three require nothing further. The others require
the assumption that heat is comparable with light in its move-
ments of reflection and refraction.
1st. conclusion: Free heat is a radiant fluid. Or, as the
surface of the body of heat becomes free, each point of the sur-
face of the body is a center to which tend, and from which are
carried, in every direction, streams of heat.
2nd. conclusion : The equilibrium of heat between two
neighboring free spaces consists in the equality of the
3rd. conclusion: When the equilibrium is disturbed, it is
reestablished by unequal exchanges, in a medium of constant
temperature, a body that is hotter or colder requires this tem-
perature according to the law that the periods of time being in
arithmetical progression, the differences of temperature are in
4th. conclusion: In a space of uniform temperatures, if a
reflecting or refracting surface is introduced it has no effect in
changing the temperature of any part of this space.
5th. conclusion: In a space of unequal temperature, if there
is placed a body which is either hotter or colder and if after-
wards a reflecting or refracting surface be introduced, the
points, upon which these surfaces direct the rays emanating
from this body, will be affected by it, being heated if the
body is hotter, or cooled if it is colder.
6th. conclusion: A reflecting body, having been heated or
cooled internally, recovers the surrounding temperature more
slowly than a nonreflector.
7th. conclusion: A reflecting body, having been heated or
cooled internally will have less effect on another body placed
at any distance (in heating or cooling it) than a nonreflector
would under the same conditions.
All these conclusions have been verified experimentally, ex-
cept that concerning the refraction of cold. This experiment
remains to be made, and I am confident of the result, at least
if the refraction of the heat is capable of being observed. This
result is indicated in the 4th. and 5th. conclusions, which could
in this way be submitted to a new test. It is hardly necessary
to indicate in this place the precautions by means of which one
would place himself beyond every kind of misobservation.
RADIATION AND ABSORPTION.
PIERRE PREVOST was born in Geneva, March 3, 1751, and died
at the same place oil the 9th of April, 1839. He was the son of
a clergyman and was educated for a clerical career, but turned
his attention to law and later to educational work. He became
a professor of philosophy and a member of the Academy of
Sciences at Berlin in 1780. Here, through his acquaintance
with Lagrange, his attention was directed to science, which
later he followed up with his studies on Magnetism and Heat
at Geneva where he became professor of physics in 1810. He
published much on different subjects, including philology,
philosophy, political economy, fine arts, etc. He issued the
works of le Sage, supplemented by many additions of his
own. His Du Calorique Rayonnant appeared at Geneva in
1809 and was an exposition and extension of his theory of ex-
changes first advanced several years before. The original
memoir and later publications appeared in the Journal de
Physique and the Phil. Trans, from 1791 to 1802. His remark-
able versatility is indicated in the variety of his publications.
His most valuable contribution to science is undoubtedly his
Theory of Exchanges one of the most important principles in
the whole range of physical science.
AN ACCOUNT OF SOME EXPERIMENTS
ON RADIANT HEAT, INVOLVING AN
EXTENSION OF PREVOST'S THEORY
Transactions of the Royal Society of Edinburgh.
Vol. XXII. Part I. pp. 120. March, 1858.
Division of Subject 23
Description of Instruments and Method . . . .24
On Radiations from plates of Different Substances . . 26
On Radiations from Polished Surf aces . . .32
On Radiations of Plates of Different thicknesses . . 33
Results Explained by Prevost's Ttieory of Exchanges . . 35
Peculiarities of the Radiation from Plates of Diatherm-
anous Substances 37
Equality of the Radiation and the Absorption . 40
Influence of the Reflective and Refractive Powers of Bod-
ies on their Radiation considered 42
Equal and Independent Radiation ..... 47
Internal Radiation and Conduction , 49
l. AN ACCOUNT OF SOME EXPERIMENTS
ON RADIANT HEAT, INVOLVING
AN EXTENSION OP PEEVOST'S
THEORY OF EXCHANGES.
BY BALFOUR STEWART, ESQ.
COMMUNICATED BY PROFESSOR FORBES.
Read, 15th, March 1858.
Division of Subject.
1. This paper consists of two parts, the first of which is
confined to describing the experiments performed; while in
the second it is attempted to connect these with certain theo-
retical views regarding Radiant Heat.
2. The experiments were made with a fourfold object; at
least for the sake of clearness, it is well to class them into four
Group L Contains those experiments in which the quanti-
ties of heat radiated from polished plates of different
substances, at a given temperature, are compared with
the quantity radiated from a similar surface of lamp-
black, at the same temperature.
Group II. Those in which the quantities of heat radiated
at the same temperature, from polished plates of the same
substance, but of different thicknesses, are compared
with one another.
Group III. Those in which the radiations, from polished
plates of different substances at any temperature, are
compared with that from lampblack at the same tem-
perature, with regard to the quality or nature of the
Group IV. Those in which the same comparison is made
between the radiations from polished plates of the same
substance, but of different thicknesses.
Instruments used, and Method of using them.
3. I am indebted to the kindness of Professor Forbes for
the use of a delicate thermo-multiplier, consisting of the sen-
tient pile, and its attached galvanometer and telescope; as
well as for much valuable information with regard to the
proper method of using the apparatus.
The following arrangement was adopted for the great mass
of the experiments:
A. Is the sentient pile, with a polished brass cone attache^
to it, for collecting the rays of heat.
B. Is the galvanometer, the position of its needle being
read to ^th of a degree by the telescope C.
D. Is a screen placed before the mouth of the cone in
which there is a small hole or diaphragm .65 inch square. The
screen is covered with gilt paper, in order that, should it get
slightly heated, it might radiate as little as possible.
The heated body is placed behind the diaphragm, filling up
the field of view from the cone ; so that every ray reaching the
cone from behind the diaphragm comes from the heated body.
RADIATION AND ABSORPTION.
In the following experiments, unless the contrary is men-
tioned, the distance of the diaphragm from the mouth of the
cone is 2 inches.
The dimensions of the cone itself are as follows :
Length of axis, or distance between centre of mouth and
pile, 5 inches.
Diameter of mouth or opening, 2.6 inches.
The temperature to which the heated body was raised was
generally 212, and the apparatus used for heating it was of the
following construction :
It consisted of a tin vessel, having its top, bottom, and sides
double (or a box within a box), and furnished on the top with
a lid, also double, by means of which the body to be heated was
introduced into the interior.
Water was poured into the
chamber between the outer and
inner boxes, and allowed to
boil ; and, when the lid was
shut, the temperature of the
interior was found to rise very
nearly to the boiling point ; a
thermometer placed in the
air of the chamber showing a
temperature of 200, and when lying on the bottom,
a temperature of 210. When an observation was to be made,
the hot body was taken out, and that surface which lay on the
bottom of the inner chamber placed behind the diaphragm, so
as to radiate into the cone. In the following experiments, un-
less the contrary is mentioned, the body has been heated in this
The first swing of the galvanometer needle was taken as rep-
resenting the intensity of the heating effect : and Professor
Forbes has shown, in a paper read before this Society, 2d May,
1836, that this will hold up to angles of about 20, which is the
maximum deviation used in these experiments.
Observations were always made with as little sunlight as pos-
sible ; and under these circumstances, it was ascertained that
the stray heat reaching the cone was inappreciable. The needle,
it was calculated, reached the limit of its swing about 12
seconds after the heated body had been taken out of the
Experiments were made to ascertain if the body cooled
sensibly during this short period of time, and it was found that
its cooling was so trifling as not to interfere in any degree with
the results of these observations. In the following experiments,
it is therefore assumed that the body remains at its original
temperature of 210 while the observation is being made.
Four observations were generally made, and three if they
agreed together exceedingly well, but never fewer. Very often
the agreement was exact. .
First Grout of Experiments described.
4. With these remarks, I proceed to describe the experiments
belonging to the first group, or those made with the view of
comparing the heat radiated from polished plates of different
substances with that radiated from a surface of lampblack at
the same temperature.
The reason why lampblack was chosen as the standard is ob-
vious ; for, it is known from Leslie's observations, that the
radiating power -of a surface is proportional to its absorbing
power. Lampblack, which absorbs all the rays that fall upon
it, and therefore possesses the greatest possible absorbing power,
will possess also the greatest possible radiating power. The first
substance compared with it was glass.
A. Glass. Apiece of plate glass, .3 inch thick, having paper
coated with lampblack pasted on its surface next the pile, gave
a deviation of 18.1. This may be taken as the radiation from
Three plates of crown glass, each .05 inch thick, placed
one behind the other, gave 17.7.
A single piece of crown glass of the same thickness,
This difference is probably owing to the single plate cooling
faster than the three plates. It may be argued that the
radiation from the glass is very nearly equal to that from lamp-
black ; and indeed this is already well known.*
* See Leslie's " Inquiry into Nature and Propagation of Heat."
RADIATION AND ABSORPTION.
B. Alum. Here the boiling- water apparatus could not be
used, since alum becomes calcined at a temperature much
below 212 ; but a self-regulating apparatus, invented by the
late Mr. Kemp, was employed instead, giving a steady
temperature of 98.
A piece of plate glass .18 inch in thickness, gave 5.0
A piece of alum of the same thickness gave 5.0
The radiation from the alum may therefore be reckoned
equal to that from glass.
C. Selenite. At the temperature of 98
A piece of selenite .125 inch in thickness gave. . . .5.1
Under the same circumstances, glass .18 inch thick
In the boiling-water apparatus,
The same piece of selenite gave 18.0
While blackened glass gave 18.5
The radiation from selenite may therefore be reckoned equal
to that of alum or glass.
D. Mica. A small box was constructed, having two windows
of mica, the thickness of the mica in the one being .0009 inch,
and of that in the other. 02 inch. This box was filled with
mercury (Professor Forbes having suggested the use of that
metal, to keep up the temperature, while interfering very little
with the radiation). The whole was then set on a glass dish in
the boil ing- water apparatus.
The radiation from the thin window was 11.2
While that from the thick window was 12.7
As it would have been manifestly erroneous to compare these
with the radiation from the blackened glass lying in contact
with the bottom of the apparatus, the thin window was
removed, and the blackened paper substituted in place of it.
While the thick mica window gave 12.7
The blackened paper gave 13.8
In comparing the radiations from the two windows, they
were observed alternately. We see, therefore, that the radia-
tion from mica, especially thin mica, is less than from lamp-
black in the proportion of 11.2 to 13.8, or the heat from thin
mica is 80 per cent of that from lampblack.
E. Rock Salt. As in the experiments with rock salt, it was
desirable to obtain results of the greatest possible accuracy, the
radiation from rock salt was not compared with that from
blackened glass ; for it was found that glass cooled more
rapidly than rock salt.
The following plan was adopted :
A piece of rock salt .18 inch thick (the temperature as
in all the previous examples being about 210, gave 3.2
A canister with water kept boiling, coated with lamp-
In order to estimate how much the rock salt had cooled
during the observation, the following experiment was made,
without any diaphragm :
Rock salt .18 inch thick taken to the cone at once,
After cooling for 15 seconds, it gave 4.9
It will be seen from this, that were the rock salt, instead of
cooling during the 12 seconds necessary for the observation,
kept at the temperature of 212 , it would not have given more
than 3.3, while the hot-water canister gave 22.0.
5. From these experiments, it appears that glass, alum, and
selenite, at low temperatures, have an intensity of radiation
very nearly equal to that from lampblack ; while mica radiates
somewhat less, and rock salt greatly less. This is shown by
the following table :
RADIATION AND ABSORPTION.
Second Group of Experiments described.
6. I now proceed to the second group of experiments, or those
designed to compare together the quantities of heat radiated
at the same temperature from polished plates of the same sub-
stance, but of different thicknesses.
A. Glass. No direct experiment of this kind was made on
glass ; for although a thick plate gave a somewhat greater
radiation than a thin plate, it was imagined that this was due
to the unequal cooling of the two plates. Indirectly, however,
we may gather that thick glass radiates somewhat more than
thin glass, from the following experiment, which belongs more
properly to the fourth group:
A plate of crown glass .05 inch thick, being placed be-
fore the cone as a screen, and a similar plate .05 inch
thick, and 3.75 inches square, being used as the
source of heat at a distance of 6 inches, and no dia-
phragm used, the deviation was 0.95*
But when the source of heat was a similar plate .10
inch thick, the deviation became 1.45
Such a difference cannot be accounted for by the unequal
cooling of the plates ; and it would seem to indicate that a small
quantity of heat from the interior of the thick plate reached
the surface ; which heat, having already been sifted by. its pas-
sage through glass, was easily able to pierce the screen.
In another similar experiment,
One piece of crown glass .05 inch thick, gave a deviation
Two plates .05 inch thick, the one behind the other, 1.55
Three such plates, 1.9
B. and C. No experiments of this kind were attempted with
alum or selenite.
D. Mica. Experiments similar to those already described,
only at a distance of 2^ inches from the cone, gave
* Without any screen, it was calculated that the intensity of effect
would have been equal to about 150.
For mica .0009 inch thick (average of two sets of experi-
men ts), 8.2
For mica, .02 inch thick (average of two sets of experi-
The experiments already quoted, which were made at a
shorter distance from the pile, gave
For mica, .0009 inch thick, 11.2
For mica, .02 inch thick, 12.7
E. Rock Salt. Three pieces of rock salt were used. Their
1st Piece. 2nd Piece. 3rd Piece.
Length 1.15 inch 2.15 inches 2.5 inches
Breadth 1.15 " 1.4 inch 1.4 inch
Thickness... .0.18 " 0.36 " 0.77 "
For these pieces, as well as for the other substances, I am in-
debted to the kindness of Professor Forbes. When placed be-
hind the diaphragm, the farthest off surface was large enough
to fill up the field of view, that is to say, all rays from the
cone striking the nearest surface struck also the surface far-
thest off ; the distance between the two surfaces being the
thickness of the piece.
The following are the means of four sets of experiments :
Radiation from 1st or thinnest piece 3.4
" ' 2nd or middle piece 4.3
" (( 3rd or thickest piece 5.3
This proves that more heat is radiated by a thick than by a
thin piece of rock salt.
The following experiments were devised by Professor Forbes,
to confirm the above results.
(a.) The second piece of rock salt was placed obliquely behind
the diaphragm, making an angle of 20 with the prolongation
of the axis of the cone. A piece of fir wood of the same dimen-
sions was placed in the same way. The two substances being
compared in this position, and also in the usual position behind
RADIATION AND ABSORPTION.
diaphragm (viz., perpendicular to the direction of the cone's
axis), the following was the result :
Oblique. Usual position.
Rock salt .36 inch thick, 4.0 4.0
Wood, same size as rock salt, 9.1 14.1
In order that this experiment may be understood, it may be
well to mention, that, when the plate was placed obliquely be-
hind the diaphragm it did not quite fill up the field of view.
Hence the wood gave out less heat to the cone in this than in
its ordinary position.
It appears, therefore, that the radiation from rock salt, in a
direction making a small angle with the surface, bears a
greater proportion to the corresponding radiation from wood
than when both radiations are taken perpendicular to the sur-
face. The reason undoubtedly is, that in the former case the
rays come from a greater thickness of the substance, so that
their intensity is increased.
P. The middle-sized piece of rock salt was bound tightly
to the thickest piece, with a slip of tin foil between, so that
the whole might cool as one piece, and thus obviate any ob-
jection that might be brought against the results, founded on
the unequal cooling of the plates, owing to their thicknesses
The surface of the middle-sized piece facing the pile,
That of the thickest piece, gave 8.1
The plates, therefore, still retain their inequality of radia-
tion; but the amount from each was increased, owing, no doubt,
to the reflection and radiation from the tin foil. The radiation
from the tin foil may be estimated at 1.0, deducting which,
we have 5.3 and 7.1; the increase now being due to reflection
from the tin foil.
7, It thus appears, that while the difference between the
radiating power of thick and thin glass is so small as not to be
capable of being directly observed, there is a perceptible differ-
ence between the radiation from thick and thin mica, and a
still more marked difference between the radiation from plates
of rock salt of unequal thickness.
But (at least with the thicknesses used) the greatest radia-
tions from mica and rock salt were still below that from lamp-
black, and the radiation from rock salt greatly so.
The following table exhibits the results of the second group
thin ) C4
Third Group of Experiments described.
8. I now proceed to consider the third group of experi-
ments, or those made with the view of comparing the radiations
from various polished surfaces with that from lampblack, as
regards the quality of the heat; its quality being tested by its
capability of transmission through a screen of the same mate-
rial as the radiating plate.
A. Glass. In an experiment already described, where a
plate of crown glass .05 inch thick was used as a screen, and
a similar plate of crown glass as a source of heat
We had , 0.95
A similar plate .1 inch thick as the source of heat,
Blackened paper attached to a similar surface of plate
glass, .3 inch thick, the blackened side being next
the pile, , 1.95
Therefore heat from a thin plate of glass is less transmissible
through glass than heat from blackened paper.
B. and C. No experiment of this nature was made with
alum or selenite.
D. Mica. The apparatus already described gave
K A D I A T 1 N AND ABSORPTION.
Without With mica screen
screen. .0025 inch thick.
For window (the window, it will
be borne in mind, is the radia-
ting surface), .0009 inch thick. .11.2 2.5
Window .02 inch thick 12.7 3.2
Blackened paper attached to
glass lying on the bottom of
the boiling-water appara-
tus, gave 21.0 6.3
We have therefore the proportion of heat passed by mica
For heat from thin mica window, 223
" " thick " " 260
" " blackened paper, 300
E. Rock salt. The thickest piece of rock salt (thickness
.77 inch) being used as a screen, and the diaphragm withdrawn,
in order to give greater results; the middle sized piece of rock
With screen. Without screen
The same screen stopped 3 rays out of 12 for ordinary lamp-
This experiment is sufficient to show that rock salt is much
less diathermanous for heat from rock salt than for ordinary
heat. The common opinion, that rock salt is equally diather-
manous for all descriptions of heat, is therefore untenable.
9. From the third group of experiments it appears, therefore,
that heat emitted by glass, mica, or rock salt, is less trans-
missible through a screen of the same material as the heated
plate, than heat from lampblack ; this difference being very
marked in the case of rock salt.
Fourth Group of Experiments described.
10. 1 now proceed to the fourth group of experiments, or
those made with the view of comparing the radiations of plates
of the same substance, but of different thicknesses, with regard
to the quality of the heat radiated.
A. Glass. It has been already shown (Art. 8), that heat
from crown glass .05 inch thick is less transmissible through
glass, than that from crown glass .10 inch thick.
B. and 0. No experiments of the kind were made on alum
D. Mica. It has been already shown (Art. 8), that heat from
thin mica is less transmissible through a mica screen than heat
from thick mica.
E. Rock salt. With a screen of rock salt .18 inch thick, the
following result was obtained :
Thickest piece of rock salt, heated to 210
(thickness .77 inch), gave 2.5
Middle-sized piece of rock salt, heated to 210
(thickness .36 inch), gave 1.7
Thinnest piece of rock salt, heated to 210
(thickness .18 inch), gave 1.1
Without any screen, the same pieces gave
Proportion of heat from thickest piece passed 51
Proportion of heat from middle-sized piece passed .41
Proportion of heat from thinnest piece passed 33
A similar experiment, with a screen .29 inch thick gave
With screen. Without screen. Proportion passed.
Thickest piece. . .2.6 5.4 .48
Middle-sized, ....1.8 4.5 .40
Thinnest 1.2 3.5 .33
It follows from this, that a screen of rock salt passes heat
from thick, more easily than heat from thin rock salt,
11. From this fourth group of experiments, we learn that heat
from thick plates of glass, mica, or rock salt, is more easily
transmitted by screens of the same nature as the heated plate
than heat from thin plates of these materials.
The following table exhibits the results of the third and
fourth group of experiments :
RADIATION A K D A B S E P T I K .
No. of Rays out of every
100 that pass through
a screen of the same
No. of Rays of
Heat out of
SOUBCE OF HEAT.
material as the source
of Heat in 1st column,
the screen being of
only one thickness for
Glass (crown ^th inch thick),
Glass (crown ^th inch thick),
Mica (thickness .0009 inch),
Mica (thickness .02 inch),
Rock salt (thickness .18 inch),
Rock salt (thickness .36 inch),
Rock salt (thickness .77 inch),
Results deducible from the foregoing Experiments.
12. These experiments, as well as others yet to be described,
may be explained by Prevost's theory of exchanges, somewhat
In the first place, it would seem to be a consequence of this
theory, that radiation must take place from the interior as well
as from the surfaces of bodies. For, suppose that we have two
indefinitely extended surfaces of
lampblack, as in the figure, and
between them a plate of rock
salt of a certain thickness, also
indefinitely extended; and let
the whole be kept at the same
temperature. Then, since the
temperature of the. rock salt
remains the same, it must radiate
as much as it absorbs. But a thicker plate of rock salt, placed
under the same circumstances, would absorb more of the heat
radiated from the lampblack because each ray would have to
pass through a greater depth of the substance of salt; hence a
thick plate of rock salt must radiate more than a thin plate.
We see likewise, the reason for the small radiative capacity of
rock salt to be its small absorptive capacity. In order to prove
this deduction from Prevost's theory experimentally true, the
following experiment was devised:
A boiling-water canister, coated with lampblack, was put
behind the diaphragm, filling up the field of view, and the
three pieces of rock salt heretofore used as sources of heat,
were now separately used as screens, being put before the dia-
phragm, so that the heat from the canister had to pass
through their substance before reaching the cone. The follow-
ing was the result:
Without any Screen of Screen of Screen of
screen. Rock salt Rock salt Rock salt
.18 inch .36 inch .77 inch
thick. thick. thick.
Eadiation from canister, 21.3 17.6 16.8 15.8
The difference between heat absorbed by plate,
thickness = .18 inch, and that absorbed by
plate, thickness = .36 inch,
Another similar experiment gives 0.9 J Mean *!
The difference between heat absorbed by plate,
thickness = .36 inch and that absorbed by
plate, thickness = .77 inch,
is 1.0 )
Another similar experiment gives 1.3 f Mean 1.1
These should nearly correspond to the differences between the
radiation from the same place, under their ordinary circum-
stances of position (if the theory be true which asserts that the
absorption of such a plate equals its radiation); accordingly we
The difference between heat radiated by
plate, thickness = .18 inch ) -.-
And that radiated by plate thickness = .36 inch, )
While the difference between radiation of
plate thickness = .36 inch }
And that of plate thickness = .77 inch, f Is 1<0
(Art. 6, mean of four sets of experiments.)
We see, therefore, that there is an agreement between the
two sets of differences, as near as can be reasonably expected.
RADIATION AND ABSORPTION.
13. If we now suppose a plate of glass, arid not a plate of
rock salt, placed between surfaces of lampblack, the plate,
whether thin or thick, will allow scarcely any heat to pass
through it; and, consequently, plates of different thicknesses
will all absorb very nearly the same amount, that is, nearly
all that enters them. In this case, therefore, the radiation
(which is equal to the absorption) will be very slightly increased
by an increase of thickness of the plate. Also the amount of
heat radiated, being equal to the heat absorbed, will be very
nearly as great as that from lampblack.
14. There are, therefore, two peculiarities of the radiation
from plates of diathermanous substances, and which are most
marked for those substances which are most diathermanons.
1st, That the amount of radiation from such plates is less
than that from lampblack.
2d, That the amount of radiation from such plates increases
with the thickness of the plate.
The correlation between these different properties of bodies
is seen from the following table:
Bodies ranked according
to their Radiating Ca
pacity (least radiating
Bodies ranked ac-
cording to their
Bodies ranked according
to the proportion by
which their Radiation
is increased by increas-
ing the thickness.
A stratum of heated gas
(from Melloni's Exper-
A stratum of gas.
15. The reason why radiation has hitherto been supposed to
be -confined to the surface, or to an exceedingly small distance
below the surface of a body now becomes obvious. The effect of
coating a surface of polished metal with gum, for instance, is
to increase the radiation; but, after a very small thickness of
film, an additional coating is powerless to increase the radiation;
the reason being, not that radiation is incapable, in all cases, of
taking place except at the surface; but because such films be-
ing exceedingly impervious to heat of low temperatures, the
radiation from them is very little increased by increasing their
Since, therefore, it appears that radiation takes place from
the interior as well as from the surface of bodies, the question
arises, are we to suppose each particle of each substance to
have, at a given temperature an independent radiation of its
own, equal, of course, in all directions ? A priori, this is the
most probable supposition, and it seems likewise to be conform-
able to experiment.
16. In an experiment already described,
A plate of crown glass .05 inch in thickness being used as
a screen, the quantity of heat radiated from crown
glass .05 inch thick that passed, was 0.95
While of that radiated from crown glass, .10 inch thick
there passed 1.45
Another experiment gave
Quantity of heat from crown glass .05 there passed . .1.1
Quantity radiated from two plates of crown glass, each
.05 inch thick the one placed loosely behind the
From this we may infer, that the radiation from two plates
of glass placed loosely behind each other is the same as the ra-
diation from a plate of double the thickness, and, consequently,
that the radiation from a particle of a substance does not di-
minish owing to its being placed in the interior.*
17. Let us now refer to the radiation from rock salt:
The radiation from a piece .18 inch thick, was 3.4
That from a piece .36 inch thick, was 4.3
That from a piece .77 inch thick, was 5.3
* The idea of this experiment was derived from a remark of Professor
Forbes, who suggested that several plates of rock salt, the one behind
the other, might be advantageously substituted for a thick plate of the
same material as giving the very same result.
RADIATION AND ABSORPTION.
Now if we suppose the radiation of a particle in the interior
to be as intense as that of a particle at the surface, why, it may
be asked (since rock salt is extremely diathermanous), does not
a piece of double thickness give nearly a double radiation and
so on, the radiation increasing very nearly as the thickness ?
If we still hold the doctrine of an equal and independent ra-
diation from every particle, we are shut up to the conclusion
that rock salt must be comparatively opaque to heat radiated
by itself, a result which is abundantly confirmed by experiment.
Thus while the radiation from rock salt .18 inch thick, with-
out any screen, is 3.4, with a screen of rock salt .18 inch thick
it becomes 1.1.
If, therefore, we have a piece of rock salt of double the
thickness, or .36 inch thick, we should expect that the radia-
tion from it would be = 3.4 + 1.1 = 4. 5. It is, in fact, 4.3. The
difference (0.2) being within the limit of error of observation.
In rock salt, therefore, we may suppose each particle to have
an independent radiation of its own, unaffected by its distance
from the surface.
18. We see, therefore, that the opacity of rock salt with re-
gard to heat radiated by itself, is a consequent of the admis-
sion, that the radiation from rock salt does not increase so
rapidly as the thickness increases ; ar.d this again results from
the fact, that the absorption of heat by a plate of rock salt
does not increase so rapidly as the thickness increases. This,
again, is due to the fact, that the first part of the plate of rock
salt sifts the heat so that it is more easily transmitted by the
second part; and this confirms the result arrived at by Professor
Forbes, who, finding that rock salt stopped heat of lower tem-
perature rather more readily than heat of high temperature,
concluded that there are a few rays for which rock salt is
* To take a numerical example, let us suppose the heat from a single
plate of rock salt to be = 1, then the heat from a plate four times the
thickness, or (which is the same thing) the heat from four single plates,
one behind another, should be nearly four times as much or = 4 (if we
suppose the heat from each of these four plates to be readily passed by
the plates between it and the pile), but the heat from the four-fold
plates, instead of being four times as much, is not double of the heat
We conclude, therefore, that every body which sifts heat in
its passage through its substance is more opaque with regard
to heat radiated by a thin slice of its own substance, than it is
with regard to ordinary heat.
19. This conclusion may be also stated thus: We have before
proved (Art. 12) that the radiation of a thin slice of any sub-
stance equals its absorption; we now add that the heat radiated
is the same as that absorbed, with regard to quality as well
For this expresses the fact, that substances which sift heat
are likewise opaque with respect to heat radiated by themselves.
For, since the heat which they absorb is manifestly that kind
of heat for which they are opaque, if the description of heat
radiated is the same as that absorbed, then they also will be
opaque with respect to heat radiated by themselves. Consid-
ering, therefore, the heat of any temperature to consist of
heterogeneous rays, we may state the law thus : " The absorp-
tion of a plate equals its radiation, and that for every descrip-
tion of heat. "
20. A more rigid demonstration may be given thus: Let
AB, and EC be two contiguous, equal, and similar plates in the
interior of a substance of indefinite extent, kept nt a uniform
temperature. The accumulated radiation from D
the interior impinges on the upper surface of
the upper plate; let us take that portion of it - A! ,
which falls on the particle A, in the direction B|
DA. This ray, in passing from A to B, will have |
been partly absorbed by the substance between
A and B, but the radiation of the upper plate being equal to its
absorption (since its temperature remains the same), the ray will
have been just as much recruited by the united radiation of the
from the single plate ; hence, the heat from any of the interior plates of
the compound plate is passed with great loss, by the plates between it
and the pile. Now, since the absorption of a plate equals its radiation,
the reason why the four-fold plate scarcely radiates twice so much as
the single one is, that it scarcely absorbs twice as much; and this again
is due to the fact, that the heat after it has passed the first plate of the
four-fold plate has become sifted, and passes with little diminution of
intensity through the other three plates.
RADIATION AND ABSORPTION.
particles between A and B, as it was diminished in intensity by
their absorption. It will therefore reach B with the same
intensity it had at A. But the quality of the ray at B will also
be the same as its quality at A. For, if it were different, then
either a greater or less proportion would be absorbed in its pas-
sage from B to C, than was absorbed of the equally intense ray
at A, in its passage between A and B. The amount of heat ab-
sorbed by the particles between B and would therefore be
different from that absorbed by the particles between A and B.
But this can not be; for, on the hypothesis of an equal and in-
dependent radiation of each particle, the radiation of the parti-
cles between B and C is equal to that of the particles between A
and B, and their absorption equals their radiation. Hence the
radiation impinging on B, in the direction of DB, must be
equal in quality as well as in quantity to that impinging upon
A; and, consequently, the radiation of the particles between
A and B must be equal to their absorption, as regards quality
as well as quantity; that is, this equality between the radiation
and absorption must hold for every individual description of
21. The following experiment illustrates this law:
The quantity of heat radiated from crown glass screen,
.05 inch thick, which passes through a crown glass
screen .05 inch thick, . . . . , = 0.95
While that from plate glass .3 inch thick, covered with
blackened paper (the blackened paper being next the
pile), which passes through the same screen. .. = 1.95
But if the surface of crown glass .05 inch thick, farthest
from the pile, be coated with paper, the polished sur-
face being next the pile, then the amount which passes
the screen, = 1.85
And if three plates, the one behind the other, of crown
glass, each .05 inch thick, be used as the source of
heat, the surface farthest from the pile of the farthest
off plate only being covered with paper, the amount
of radiation which passes the screen, = 1.95
Such a plate of glass or series of plates, therefore, by having
the farthest off surface coated with paper, gives out heat
similar to that from paper or lampblack; the reason being,
that the heat from the paper on the farthest off surface is as
much recruited as it is absorbed by its passage through the
glass, both as regards quantity and quality; so that the radia-
tion which falls upon the cone is virtually that from paper or
23. There is little difficulty in explaining why heat from a
thick plate of any substance should pass more readily through
a screen of the same substance than that from a thin plate.
The reason is, that the heat from the interior of the thick
substance, having been sifted in its passage, is, therefore, now
more easily able to pass through a screen of the same substance.
23. We see also why, generally speaking, bodies at the same
temperature radiate the same quality of heat; let us, for in-
stance, take a tolerably thick plate of glass, and a surface of
lampblack, and compare them together. Since the plate of
glass absorbs nearly all the rays that fall upon it, it will radiate
nearly as much as lampblack; and since the quality of the
radiated is the same as the quality of the absorbed heat, its
radiated heat will very nearly have the same quality as that
which is radiated by lampblack.
Tlie influence of the Reflective and Refractive Powers of Bod-
ies on their Radiation considered.
24. Hitherto in these investigations no account has been taken
of reflection at the surfaces of the plates, because 1st, those rays
only were considered which passed perpendicularly, or nearly so,
through such plates ; and, 2d, because the indexes of the re-
fraction for the substances experimented on were not very high.
But for rays passing obliquely through such media, or for
rays passing in any direction into substances such as metals, we
must take account of reflection from the surface which will in-
fluenoe materially our results.
Thus, no substance is so opaque for heat as metals, but yet
only a small portion of the heat falling on them is absorbed,
the rest being reflected back ; consequently for such bodies the
radiation (which must be equal to the absorption) is very small.
It is also desirable, for another reason, to investigate the
laws according to which the reflective nature of the surface of
RADIATION AND ABSORPTION.
a body influences its radiation. For the question arises, is the
law of an equal and independent radiation of each particle of a
body theoretically consistent with equilibrium of temperature ?
That is, suppose we have an irregularly-shaped inclosure walled
round with a variety of substances, and each particle of each
substance radiating into the inclosure, from the sides of which
it is reflected many times backwards and forwards before it is
finally absorbed ; this being the case, will the law of equal and
independent radiation, and those of reflection and refraction,
so fit with one another, that every particle of the walls of the
inclosure shall absorb precisely as much heat as it radiates ?
It will be endeavored to show that these laws are so adapted to
each other ; and I shall select for the proof a definite form and
description of inclosure, the conclusions arrived at rendering it
highly probable (if not rigidly demonstrating) that the same
adaptation will hold good for every inclosure, however irregular
For these reasons, I shall now endeavor to investigate what
connection the radiation of a substance has with the reflective
power of its surface ; and in doing so (in order to abstract
entirely from the effects produced by the variable thickness of
the radiating plate), I shall suppose it to be of indefinite thick-
ness ; so that all the heat which enters it is absorbed. Our
consideration is, therefore, limited to the effects of one surface.
25. Let AB be a portion
Lam p B!ack of the line of section of an
indefinitely extended sur-
face with the plane of the
paper supposed perpendicu-
lar to the surface, and let
this surface belong to a
body (M) of indefinite
thickness downwards ; also
let there be an indefinitely
extended surface of lamp-
black parallel to this lower surface, as in the figure. Lastly,
let the whole be kept at uniform temperature. In order that
the body (M) may be maintained at this temperature, it is
necessary that the heat which has left the surface AB, having
come from the interior of (M), in the direction contaiued*in
any very small angle CAD, shall be replaced by an equal quantity
of heat entering the surface AB, to diverge into the interior
through the same small angle CAD. For, by this arrangement
it is clear the particles in CAD get back as much heat as they
Part of the heat, no doubt, which fell on A in any direction
DA, would be reflected back in the direction AD', making the
same angle with the surface as AD ; but this loss would be
made up for by part of the heat falling upon A, in the direction
D'A, being also reflected back in the direction AD.
The internal reflection at A being compensated for, if the
heat that really leaves the medium be also compensated for,
then as much heat will be passing at A in the direction AD as
will be passing in the direction DA. It will be the same,
therefore, as if the body, instead of having a surface at A,
were indefinitely extended upwards from A, as well as down-
ward ; in which case, as has been already shown (Art. 20), there
will be equilibrium of temperature, provided that the radiation
of a particle is equal to its absorption, and that for every des-
cription of heat.
Before proceeding further with this investigation, it will be
necessary to establish some preliminary propositions.
26. 1st Preliminary Proposition.
The heat which falls on the line AB in the directions con-
tained in the very small angle CAD, is
the same which falls on AE, perpendic-
ular, EB, through the same very small
angle. For every ray which fell on AB
passed through AE, with the exception
of a small quantity which passed through
B EF ; but the angle EBF being very
small, EF is very small compared with AE, and consequently
the heat falling on EF may be neglected in comparison with
that falling on AE.
It is clear, also, that the heat falling on AB is proportional to
AB, and to the size of the very small angle CAD.
The above will still hold if, instead of the substance of which
AB is the surface being supposed below AB, and the rays fall-
RADIATION AND ABSORPTION.
ing on it through a vacuum, we suppose a substance to be
indefinitely extended upward and the rays to originate in the
substance itself, and fall on its surface AB.
For, although any ray GE, which falls on E, will be partly
absorbed between E and B, it will be as much recruited by the
united radiation of the particles between E and B as it was
absorbed ; so far, indeed, as regards quality and intensity (from
what has been already proved, Art. 20), we may consider such
a ray to be traversing a vacuum, it being recruited just in pro-
portion as it is absorbed.
It is evident, also, that in this case the quantity of heat fall-
ing on AB will be proportional to the size of the very small
27. 2d Proposition.
First case. If AB represent a surface (the substance being
below AB), and OF a surface of lamp- c p G F
black indefinitely extended (as in Art.
25), from which rays fall on AB through
a small angle CAD ; then, if AE be
drawn perpendicular to GB, the heat
that falls on AB will = a const. X AE,
whatever be the value of the angle CAB.
For, since the angle CAD is exceedingly small, CD may be
considered very small in comparison with CF or CG ; therefore
the heat which impinges on AB through the angle CAD may
be taken to be that which radiates from CG in direction between
CA and DA; but since the radiative power of lampblack in
any direction varies as the sine of the angle which that direction
makes with the surface, this will = const. X AE. Hence, if
R X CAD be the quantity of heat which falls on AB, when AB
is perpendicular to GB, that which falls on it when GB makes
any angle GBA with AB. will be R X CAD sin GBA.
If i denote the angle which GB makes with the perpendicu-
lar to AB, then the heat impinging on AB will be R cos i
2d case. If the substance be above AB, and the rays falling
on AB originate in the substance, the same formula will hold,
for it has been shown, in Prop. 1st, that in this case, the heat
falling on AB through the small angle CAD = that which falls
on AE through the same small angle; but, since the radiation
from the interior of the substance is the same in all directions
(each particle radiating independently and equally in all direc-
tions), the amount falling on AE will not be aifected by the
angle which AE makes with the surface; hence the heat falling
on AB = const. X AE = const. X sin GBA.
If R' X CAD = quantity which falls on AB when AB is per-
pendicular to GB, that which falls on it when GB makes any
angle GBA with AB, will be R' X CAD sin GBA ; also the
expression corresponding to R cos i' x CAD will be R' cos i'
28. 3d Proposition. Let a ray strike the surface of a me-
dium, at an angle of incidence = i; and another ray at an angle
of incidence i + 6 i, it is required to find the difference between
the two angles of refraction.
Let p be the index of refraction, then,
sin i== fj. sin i'
Hence, 6 (sin i) = p 6 (sin if)
cos i 6 i = ft cos i' 6 i'
TT ., cos i
Hence, 6 ^ - r,s i
29. I shall also make the following supposition with regard
to the laws of reflection and refraction.
1st. That if Q represent the quantity of heat falling on the
surface of a medium in any direction CA, and
0Q be the quantity reflected, then (1 a) Q is the
quantity of heat refracted into the medium in
the direction AC 7 . This follows from the law of
the conservation of vis viva.
2d. That if the same heat Q originate in the
Ic 1 medium, and strike A in the direction C'A,
the quantity reflected back into the medium will be #Q, and
the quantity refracted out in the direction AC will be (1 a) Q.
30. These preliminary propositions being established, and
suppositions made, let us suppose that heat from the surface of
lampblack strikes the surface AB of the indefinitely thick me-
dium (Fig. Art. 25) through a small angle 6i (i being the angle
of incidence), by Prop. 2d. the Quantity of this heat will
RADIATION AND ABSORPTION.
be R cos idi; while the part of it which enters the substance
we shall call (1 a) R cos i 6 i. These rays will diverge in the
substance through an angle 6 i'= ^ r 6 i (Prop. 3).
p COS I
But the quantity of heat that falls on AB from the interior
through this angle will be
R' cos idi' = R' cos i' - u c * s \, *i = ~- cos iti,
and the portion of this which leaves the medium will be
(1-a) R' cos ;' di
Equating this with (I a) R cos 161, which enters the me-
dium, we have = R or R '= /" R. With this supposition,
therefore, the law of an equal and independent radiation of
each particle will give us equilibrium of temperature in the
particular case under consideration. Had R' been a function
of i', it would have shown that the law of an equal an inde-
pendent radiation was inconsistent with equilibrium of tem-
31. Only part, however, of the heat from the lampblack
falling on AB entered into the medium, a portion of it = a R
cos i 6 i being reflected back to the lampblack, hence the total
quantity of heat radiated and reflected which leaves the surface
AB through the small angle di will be = R cos i 6 i, the same as
if the substance had been lampblack, the only difference being,
that, in the case of lampblack, all this heat is radiated,
whereas in other substances only part is radiated, the remainder
being reflected heat.
32. Although we have considered only one particular case,
yet this is quite sufficient to make the general principle plain.
Let us suppose we have an enclosure whose walls are of any
shape, or any variety of substances (all at a uniform temper-
ature), the normal or statical condition will be, that the heat
radiated and reflected together, which leaves any portion of the
surface, shall be equal to the radiated heat which would have
left that same portion of the surface, if it had been composed
of lampblack. And, indeed, we may see, from what has been
already proved, that should such a state of things only once
take place, it would always remain, there being no disposition
to alter it.
Let us suppose, for instance, that the walls of this enclosure
were of polished metal, then only a very small quantity of heat
would be radiated ; but this heat would be bandied backwards
and forwards between the surfaces, until the total amount of
radiated and reflected heat together became equal to the radia-
tion of lampblack.*
33. The equation R' = //R must necessarily hold for every in-
dividual description of heat. We have, therefore, two laws
necessary to the equilibrium of temperature 1st, That the
absorption of a particle is equal to its radiation, and that for
every description of heat ; 2d, That the flow of heat from the
interior upon the surface of a substance of indefinite thickness,
is proportional caeteris paribus to its index of refraction and
that for every description of heat. It will, however, be borne
in mind, that the former of these laws has been verified by ex-
* This will be clearly seen if we consider only those
rays that are radiated perpendicular to the surface
to the case of two parallel plates of polished metal
~~ of the same description radiating to one another.
For let r be the common radiation of the point C in direction CD, and
of the point D in the direction DC, then since these radiations are
bandied backwards and forwards in the directions CD, DC. until they
are extinguished, we have the total quantity of heat falling on D in the
direction CD (if ar denote the proportion of r reflected after one single
reflection) expressed as follows:
Total heat radi- J ( r+aV+aV+etc, ) = r(l+a+^+a 8 )
ated and reflected, P4 + ar +a 8 r+ B r+etc. f = (since a < 1)
falling on D, ) ( ) 1 a v
But 1 a denotes the absorptive power of the metallic surface (all the
heat not reflected being absorbed). Hence, since the radiative powers
of bodies are proportional to their absorptive powers (Leslie's Inquiry)
1 being the absorptive power of lampblack, the perpendicular radiation
of a lampblack point will be = which is the very same expres-
sion we have obtained for the total heat radiated and reflected together,
falling on D, in the same perpendicular direction from the metallic
E AD I ATI ON AND ABSORPTION.
periment, while the latter is only deduced from a theoretical
investigation. It will also be seen, that by increasing the
thickness of the radiating plate indefinitely, the radiation be-
comes ultimately independent of the diathermancy of the plate
and is regulated only by its refractive index.
34. The connection which we have attempted to trace be-
tween the refractive and radiative power of a substance, pre-
sumes that those rays which we have been considering, have the
power of forming wave lengths with the medium under con-
sideration ; that is, of being capable of proper reflection and
It may be, however, that glass and other similar substances
are so opaque, with respect to most of the rays of heat of low
temperature, as to stop them almost entirely at the surface.
As such rays may, therefore, be conceived to be absorbed
within the limit of physical surface of the medium, the cor-
responding radiation may be conceived to proceed from this
physical surface. To such a case we may perhaps suppose reason-
ing similar to that of Fourier (as given by Professor Forbes
in the Philosophical Magazine for Feb., 1833,) to be applicable ;
the intensity of radiation being therefore proportional to the
sine of the angle which the direction makes with the surface.
35. Let us now see, in conclusion, whether these investiga-
tions seern to point out any connection between internal radia-
tion and conduction.
Now, without in the least confirming that these are identical
there seern to be two points of similarity between them.
1st, Since the heat which enters metals is all absorbed at a
very small depth, it follows that the flux of radiant heat from
within upon the interior of metallic surface is derived from a
very small depth.
Also, if we allow (what it has been endeavored to prove, Art.
30) that the flux of heat upon the interior of the surface is pro-
portional to the index of refraction, this flux will be greatest in
the case of metals which may be supposed to have a very high
refractive power ; besides which, it will, as we have seen, be
derived from a very small depth. The radiation of a metallic
particle is therefore very great.
Now, if internal radiation be in nny way connected with con-
duction, we might expect that good conducting substances
should also be good internal radiators of heat, and we see they
2d, The second bond of similarity is this. It seems to be a
law that substances are almost invariably more diathermanous
for heat of high temperature than for heat of low ; consequently,
at high temperatures, the radiation of a thin plate or particle
of a substance will bear a smaller proportion to the total lamp-
black radiation of that temperature than at low temperatures.
The internal radiations of particles of bodies would therefore
diminish at high temperatures (not absolutely, but with respect
to the proportion which they would bear to the total radiation
of these temperatures). If the same rule holds for metals, and
'conduction be connected with internal radiation, we should ex-
pect that at high temperatures the conducting power of metals
would be less than at low temperatures. Now this has been
proved to be the case by Professor Forbes.
RESEARCHES ON RADIANT HEAT.
Transactions of the Royal Society of Edinburgh.
Vol. XXII, PL I. pp. 5973. April, 1859.
Division of Subject . \ . . . . . , : 53
Instruments used and Method of Investigation . . .53
Effect of Roughening the Surface of a Body upon its Radi-
ation . . . . . . . . .53
Nature of the Heat Radiated by Rock Salt . . .56
Radiation of Glass and Mica at high Temperatures ... 59
On the Law which Connects the Radiation of a Body ivilh its
Temperature . . . . . . .s .. .64
On General Diathermancy . . . . . , .69
VI. RESEARCHES ON RADIANT HEAT.
BY BALFOUR STEWART, M. A.
COMMUNICATED BY PROFESSOR FORBES.
(Read April 18th, 1859.)
Division of Subject.
1. The first part of this paper describes the following groups
of experiments :
Group I. On the effect which roughening the surface of a
body produces on its radiation.
II. On the nature of that heat which is radiated by
rock salt at 212 F. .
III. On the radiation of glass and mica, at high tem-
The second, or theoretical, portion of the paper, has refer-
ence to the law which connects the radiation of a particle with
its temperature and to Dulong and Petit's experiments on this
There is also an addition of a later date than the rest of the
paper on General Diathermancy.
Instruments used, and Method of Investigation.
2. The instruments used, and the method of using them,
were much the same as described in the first series of these re-
searches, Art. 3. Should any difference occur in the method of
conducting a particular experiment, it will be mentioned when
the experiment so performed comes to be described.
First group of Experiments Described.
3. This group of experiments has reference to the effect of
roughening the surface of a body upon its radiation. This was
suggested to the writer by Professor Forbes. The first sub-
stance tried was rock salt.
A. Rock salt. It was found that roughening the surface by
means of emery paper, until it became quite dim, had little or
no effect in increasing the radiation, as will be seen from the
following statement embodying the mean result of three sets of
The pieces used were the middle piece (thickness =.36 inch)
and the thickest piece (thickness = -77 inch), described in first
series, Art. 6. These pieces were placed at a distance of about
four inches from the mouth of the polished brass cone, and in
order to increase the effect, no diaphragm was used. They
were heated in the boiling-water apparatus already described.
With this arrangement
The thick piece gave, when polished, a deviation of .21.!
when roughened, 21.8
The middle piece gave, when polished, a deviation of .13.6
when roughened, 13.5
4. The next point was to ascertain if roughening had any
effect upon the quality of heat radiated.
The following table will show that it does not alter the qual-
ity of the heat sensibly; its quality being tested by its capacity
of penetrating a screen of rock salt.
SOURCE OF HEAT.
Percentage of whole
which penetrates a Rock
Salt Screen thickness .29
.77 inch thick,
.36 inch thick,
*In the experiments with roughened surfaces, only one of the sur-
faces of the substance was roughened, the other being left polished.
In radiation experiments, therefore, the roughened surface was placed
next the pile; while in transmission experiments it was placed furthest
from the pile.
RADIATION AND ABSORPTION.
The trifling difference between polished and roughened salt
in this table may fairly be attributed to error of experiment.
We may therefore conclude, that roughening by emery paper
neither alters the quantity nor the quality of the heat radiated
by rock salt.
5. Again, the transmissive power of rock salt for lampblack
heat of the temperature 212, is not sensibly altered by rough-
ening the surface. This will be seen from the following state-
The percentage of Lampblack
heat transmitted was
With Screen of Rock salt, thick-
ness .36 inch, polished, 77
With Screen of Rock salt, thick- *
ness .36 inch, roughened, 77
This result naturally follows from the previous one, for it
has been shown (First Series, Art. 19) that the absorption of a
plate equals its radiation and since roughening its surface does
not influence the radiation it ought not to influence the absorp-
6. B. Glass. It is already known that roughening the
surface of a plate of glass does not sensibly increase its radia-
tion. It is only necessary, therefore, to ascertain whether
roughening the surface of a radiating plate of glass alters the
capacity of its heat for penetrating a screen of glass. Accord-
ingly, a plate of crown glass .05 inch thick, 3.75 inches square
being placed before the cone as a screen, and a similar plate
roughened, heated in the boiling-water apparatus, being used
as the source of heat, and no diaphragm used,
The deviation was 1.0
When the source of heat was a similar plate, .10 inch
thick, the deviation became, 1.5
And lastly, when the source of heat was a plate
covered with lampblack, the deviation was, 1.9
With the same sources of heat, only the glass polished in-
stead of being roughened, these numbers were 0.95, 1.45,
1.95. From the correspondence between these two sets of re-
sults, we may infer that the quality of the heat radiated by
glass (at least in so far as transmission through a plate of glass
can test it) is not altered by roughening the surface of the
7. And from all these experiments, we may infer (what has
indeed been already remarked by Professor Forbes), that
although roughening its surface with sand or emery paper ren-
ders a body dim for light yet it still remains specular for heat
rays, which, possessing a greater wave length than those of
light, are less liable than the latter to be influenced by scratches
Second Group of Experiments Described.
8. The second group of experiments has reference to
the nature of the heat which is radiated by rock salt at 212.
Its quality being tested by transmission through
a. A screen of mica.
/?. One of mica split by heat.
7. One of glass.
9. a. Mica Screen. By the mean of three sets of experi-
ments, a mica screen (thickness = .003 inch nearly) passed
about 31 per cent of ordinary lampblack heat, while it only
passed 18 percent of rock salt heat. Or if we call the proportion
of black heat passed by the mica 100, that .of rock salt heat will
10. /5. Split Mica Screen. Two sets of experiments agreed
in giving twenty per cent as the proportions of lampblack heat
of 212, transmitted through a screen of mica split by heat,
while the proportion of rock salt heat transmitted by the same
screen was only 15^ per cent. These numbers are to one
another as 100 to 76.
11. y. Glass Screen. In order to avoid secondary radiation
from the screen, which, in this case, absorbs nearly all the
heat, two screens of microscopic glass were used, the one be-
hind the other, with an interval between.
Moreover, as in this case, the proportion of heat transmitted
is exceedingly small, the following arrangement was adopted to
make it measurable.
The experiment consisted of four parts,
1st. The effect of rock salt heat upon the pile without a
screen was observed by the ordinary galvanometer.
RADIATION AND ABSORPTION.
2d. The effect of lampblack heat, also without a screen,
was observed by the same galvanometer.
3d. The wires of the pile were then transferred to a more
sensitive galvanometer, and the effect of lampblack heat
observed, the glass screen being interposed.
4th. The sensitive galvanometer and glass screen being re-
tained, the effect of rock salt heat was lastly observed.
By this method of experimenting, it was merely the relation
between the diathermancy of the screen for lampblack heat
and for rock salt heat that was measured; its absolute diather-
mancy for either of these heats not being determined. Two
sets of experiments, conducted in this manner, gave the fol-
By the first set, calling the proportion of the whole lamp-
black heat which passed the screen 100, that of the rock salt
heat which passed the same screen was 54. And by the second
set, these numbers were 100 to 60.
12. As in these experiments with a glass screen the propor-
tion of heat passed is very small, great numerical accuracy
cannot be looked for and the results obtained are valuable
rather as determining the direction and character of a fact,
than as measuring the extent to which it holds.
13. It is already well known that rays of great ref rangibility
or small wave length pass through glass and rnica more readily
than those of an opposite character. The difficulty with
which rock salt heat penetrates these substances as compared
with ordinary heat might therefore lead us to infer that the
wave length of this heat is greater than that of ordinary lamp-
14. If, therefore, the heat radiated by rock salt is of great
wave length since (First Series, Art. 19) 'the quality of the
heat radiated is the same as that of the heat absorbed, it follows
that the heat most absorbed by rock salt must be heat of great
wave length; and this derives confirmation from a fact noticed
by Professor Forbes, viz., that rock salt passes a somewhat
greater proportion of heat of high temperature than of that of
low; heat of high temperature possessing a less average wave
15. If we look now to the relative transmission of the two
descriptions of heat through mica split by heat, we see that
the facility of transmission is yet in favor of ordinary heat, but
not so strikingly as with a screen of common mica. This will
be seen from the following table :
NATURE OF SOURCE.
Transmission of Or-
dinary Heat, at
Rock salt Heat
at 212 F.
Mica split by heat
Compare this with the following table deduced from the
results given by Professor Forbes, in the Fourth Series of his
Researches, Art. 9.
NATURE OF SCREEN.
Transmission of Heat
from Blackened Brass
at 700 F.
at 212 F.
iSlica 015 incli thick
From a comparison of these two tables, it will be seen that,
as tested by the two substances, mica and mica split by heat,
rock salt heat at 212 F bears to ordinary heat of that temper-
ature a relation similar to that which ordinary heat at 212 F
bears to heat at 700 F; that is to say, that just as heat of 212
F has a greater wave length than heat of 700 F, so rock salt
heat at 212 F has a greater wave length than ordinary heat at
that temperature. And the surface stoppage produced by
splitting the mica,* telling most powerfully upon heat of high
temperature, or small wave length, while the stoppage by sub-
stance is in the opposite direction, we see how the one effect
tends, to a certain extent, to neutralize the other, rendering the
proportions of different kinds of heat passed by split mica more
nearly alike than those passed by ordinary mica.
16. All these experiments concur in showing that heat from
rock salt possesses very great wave length, and probably heat
from a thin plate of this substance, at a low temperature, may
HAD I ATI ON AND ABSORPTION.
be found to possess a greater average wave length than any
other description of heat which can be exhibited.
Third Group of Experiments Described.
17. I now proceed to describe the third group of experiments,
or those on the radiation of glass and mica at high tempera-
A. Glass. For the experiments on glass, the following
apparatus was used: The pile was placed within a box, and
surrounded with cotton wadding. The orifice through which
radiant heat was admitted into the box consisted of a brass
tube AB, blackened in the
inside. The diameter of this
tube was inch, its length 3
inches, and during the
greater part of its length it
passed through water, con-
tained in the chamber CEFD. The side of the box (CAD) next
the pile was lined with tin foil. Owing tothesmall divergence
of the rays of heat which hud to pass through the narrow tube,
the cone might be placed several inches to the left of A without
sensibly weakening the effect, and, on the other hand, the
source of heat might be placed some distance to the right of D
without ceasing to fill up the field of view. By this means, the
distance between the pile and the source of heat being consider-
able, no currents of heated air from the latter would be able to
reach the former; and as the tube AB was blackened in the in-
side, and passed through water, reflection and secondary radia-
tion would both be avoided. By means of a lid fitting on the
tube at A the aperture might be diminished at pleasure. The
pile was connected with a very sensitive galvanometer.
When glass at a high temperature was the source of heat,
a very small aperture was sufficient, and thus the advantage was
gained of having the whole field covered with glass, all at a
high temperature, which could not have been the case had the
aperture been large.
Slips of glass about inch broad were used, and were set ver-
tically, just touching a gas flame from a Bunsen's burner.
When two slips one behind the other were used, the one
just touched that portion of the flame next the pile, and the
other that portion furthest from it. A cross section of the
arrangement is shown on page 59.
A single slip of glass about .1 inch thick thus heated gave a
deviation of 16. 5, while two slips, the one behind the other,
gave 18. 5. When the slips were .05 inch thick these numbers
were 29 M and36.3.
18. From these experiments we may conclude, that at a
high temperature, 700 or 800 F, the radiation from two
plates of glass, one behind the other, is sensibly greater than
that from one a result which does not hold for glass at 212.
Or the fact may be stated thus:
The radiation of a single plate of glass bears a smaller pro-
portion to the total radiation of 700 than at 212.
19. It was next tried whether the capacity of a glass screen
for passing heat from blackened copper at 700 was altered by
its being heated.
In order to ascertain this, blackened copper at 700 F was
placed behind a slip of glass, and the amount of heat from the
copper which passed the glass was observed.
Firstly, When the glass was cold.
Secondly, When it was heated to between 700 and 800 F.
20. As in these experiments the considerably fluctuating
temperature of the source of heat causes a somewhat large
difference between successive observation, and renders necessary
a great number in order to arrive at a correct result, it was
thought desirable, instead of using momentary deviations, to
employ permanent ones. This was done with complete success;
the application of the heated copper, or its removal, causing an
unmistakable alteration of the position of the needle.
21. The experiment was then varied in the following man-
ner: The needle was kept permanently deviated by the heated
glass, and the momentary swing due to the application or with-
drawal of the heated copper was noticed, and was compared
with that occasioned by the hot copper when the glass was cold
and the needle at zero.
22. These experiments, which are not, perhaps, individually
susceptible of very great exactness, agreed, however, in render-
ing it probable that glass, owing to its being heated up to
RADIATION AND ABSORPTION.
about 700 F. does not change its diathermancy for heat of
23. B. Mica. The experiments on mica were made with
the ordinary galvanometer. A piece of mica, thickness about
.008 of an inch, being used as a screen, and a diaphragm, .65 of
an inch square, at the distance of three inches from the mouth
of the pile, being employed, the mean of two sets of experiments
made the proportion of black heat of 200 F passed by the
mica to be 13 per cent. Placing an additional diaphragm of
the same size 3| inches beyond the first, and using as a source the
temperature of 400 F, the mean of two sets of experiments
made the proportion of heat passed by the mica screen to be 21
In order to test whether the apparently greater diathermancy
of the screen for heat of 400 F was owing to the difference in
the nature of the heat, or to the heat at 400 F striking the
screen more nearly at a perpendicular incidence, and thus
experiencing less reflection as well as passing through a smaller
thickness of mica, an experiment was made on heat at 200 F,
with the arrangement and distance used for heat of 400 F,
which seemed to show that this difference of distance does not
affect sensibly the proportion transmitted. We may therefore
conclude that the difference in proportions transmitted is ow-
ing to a difference of quality in the two descriptions of heat.
24. A cast-iron box was next constructed having this same
plate of mica inserted as a window, so that, while one side of
the box consisted merely of a moderately thin plate of cast-
iron, the other, except round the edges, was composed of mica.
The cast-iron side was then blackened, and the box filled with
mercury. A thermometer inserted in the box measures the
temperature. At 200 F, with the usual diaphragm three inches
from the mouth of the pile, the proportion between the radia-
tion of the blackened side and the mica window was, by the
mean of three sets of experiments, as 100 to 87.8, while at
400 F, with the usual arrangement of two diaphragms, the
same proportion was 100 : 84.1.
25. Let us endeavor to discuss these results. The radiation
from the mica window consists of three portions :
a. The proper radiation of the mica plate.
/?. That portion of the radiation of the mercury which has
been able to penetrate the mica plate.
y. That portion of the radiation of the mica which, strik-
ing upon the mercury, is reflected back by it and has pene-
trated the mica plate.
Now, supposing there was no mercury behind the mica, and
that rnica between 200 and 400 does not alter its diathermancy
as a screen in any respect, let us inquire what ought to have
been the result obtained. Then, since the radiation of a thin
plate equals its absorption (First Series, Art. 19), and since
the absorption of this mica plate was 8 per cent less at 400
than at 200 (Art. 23), its proportional radiation ought to be
8 per cent less at 400 than at 200.
26. But the effect of the mercury behind the mica mani-
festly tends to diminish this difference. For we know that
the mica (Art. 23) passes 8 per cent more of lampblack heat at
400 than at 200 ; it will therefore no doubt pass a greater pro-
portion of the heat from the mercury behind at 400 than at
200. But we have reason to think that the radiation of mer-
cury is nearly %' of that of lampblack.* Consequently we
may suppose that owing to this action of the mercury, the pro-
portional radiation of the mica window at 400 is increased
about y of 8, that is, 2 percent. This reduces therefore the
difference from 8 to 6 per cent.
27. But the mercury acts in another manner also in the
same direction. Had mercury been a perfect reflector, its
presence behind the mica would have been equivalent to doub-
ling the thickness of the plate ; for it would have sent the
whole radiation of the mica that fell upon it back through the
mica. But the difference between the proportional radiation at
200 and at 400 is less for a thick plate of mica than for a thin
one (indeed, when the plate is indefinitely thick, this difference
vanishes, and the proportional radiation is the same at all tem-
peratures); this action of the mercury, therefore, would tend
still further to diminish the already diminished difference of
* Provostaye and Desains estimated the proportion of heat reflected
by mercury to be 77 per cent. The radiation, being complementary to
this, may be reckoned to be 23 per cent nearly.
RADIATION AND ABSORPTION.
6 per cent. The amount of this action cannot be far from
3 per cent, * in which case the 6 per cent would be reduced
to 4 per cent ; now 3.7, or, in round numbers, 4 per cent is the
observed difference between the proportional radiation of the
mica window at the temperatures 200 and 400.
28. We see thus that the behavior of the mica as a screen,
compared with its behavior as a radiator, agrees very well with
the supposition which we made in Art. 25; viz., the mica between
the temperatures of 200 and 400 does not alter its diather-
mancy in any respect; a result similar to that which we have
already deduced for glass (Art. 22) between somewhat wider
29. Experiments with the same object in view, but of a
more direct description, were made upon mica, similar to those
already described as having been made upon glass, that is, it
was endeavored to ascertain whether hot mica passed as much
heat from hot copper as cold mica; but in these experiments
the fluctuation was very considerable, probably owing to the
small body of the mica. Nevertheless, they confirmed the
results above obtained ; viz., that mica does not change its
diathermancy in any respect owing to its being heated.
30. We may therefore conclude that this property (at least
within moderate limits) is common both to glass and to mica,
and indeed, a priori, there appears no good reason why the mere
heating of a substance should change its diathermancy. It is
the theoretical importance of this property that has induced me
to take pains to verify experimentally and its importance will
be seen from some of the consequences which follow its estab-
lishment, which I shall now proceed to discuss.
* It would have been better to have tested, by means of a direct exper-
iment, to what extent the difference between the proportional absorp-
tion and radiation of mica at 200 F and at 400 F would have been
diminished by doubling the thickness of the plate; but unfortunately
the plate of mica was so much cut up by being used as a window, as to
be unfit for being formed into a double screen.
We see, however, from Art. 37, that while the difference between the
proportional radiation of a plate of glass (thickness imm) at 100 C and
and 390 C is 9 per cent, the same difference for a plate of double the
thickness is only 7 per cent, or 2 per cent less. We may, therefore, with-
out much risk of error, adopt this difference of 2 per cent for mica un-
On the Law ivhich Connects the Radiation of a Body with its
31. The experiments of Dulong and Petit upon the cooling of
two thermometers, one naked, and the other covered with silver,
seemed to show that the proportion between the radiations of
these two substances was the same at the different temperatures
Now I have endeavored to prove in these researches 1st,
That the radiation of a thin plate at any temperature equals its
absorption of black heat of that temperature. 2nd, That the
diathermancy of glass and mica (and probably of other
substances) is not altered by heating the substances. Again, it
is well known that substances are generally more diathermanous
for heat of high, than for heat of low temperature; it follows
that the radiation of a thin plate of a substance at a high
temperature should bear a less proportion to the total radiation
of that temperature than at a low temperature.
32. While, therefore, it is likely that the radiation of a
silvered thermometer (silver leaf being quite opaque for all
heat) will bear a constant relation to that of a blackened
thermometer at all temperatures, we should expect that for a
naked thermometer, just as for the mica window, the radia-
tion should bear a somewhat less proportion to the total radia-
tion at a high temperature than at a low. We should therefore
expect the radiation of the naked thermometer to increase
somewhat less rapidly with the temperature than that of the
silvered thermometer. Dulong and Petit, nevertheless,
found the rate of increase to be the same for both.
33. Now, in the first place, since glass is exceedingly
opaque for heat even of 300 C (the highest temperature ex-
perimented on), the difference we are in search of (analogous
to the diiference of four per cent in the mica window) would
be exceedingly small. But, in the second place, Dulong and
Petit had two thermometers, one of which, containing about
three pounds of mercury, was used for high, and the other and
smaller one for low temperatures. This latter circumstance
will complicate or even vitiate their experiments so far as re-
gards this peculiar difference we are treating of.
RADIATION AND ABSORPTION.
34. Although, for these reasons, attaching little importance
to Dulong's and Petit's observations, so far as varying diather-
mancy is concerned, yet it may be well to state that they show, on
the whole, a very small difference in the direction which would
indicate a superior diathermancy of the glass at a high tempera-
35. Assuming it proved that the proportional radiation of a
thin plate is less at a high than at a low temperature, I shall
now endeavor to show that this difference increases as we
diminish the thickness of the plate. To prove this, it is only
necessary to exhibit the following table, given by Melloni :
NUMBER OF RAYS OUT OF 100 PASSED.
at 390 C.
at 100 C.
36. We have already seen that glass does not change its
properties with regard to heat, by being raised to the tempera-
ture of 390 C ; it is perhaps, however, too much to conclude,
that when heated to the temperature of a Locatelli lamp, its
properties would remain unchanged. At all events, in order to
make use of the whole of the above table, we may suppose the
properties of the glass to remain the same throughout, es-
pecially as the results we shall deduce from the supposition
will be of the same nature as if we had only extended it to glass
at 390 C.
37. Presuming, therefore, that the diathermancy of glass does
not alter through its being heated, and allowing 4 per cent as
the proportion of the heat striking it reflected from the first
surface of a glass screen, and supposing also the same propor-
tion of the heat which is able to reach the second surface to be
reflected from it, we may, on the principle that the propor-
tional radiation of a plate equals its proportional absorption, con-
struct the following table :
PROPORTIONAL RADIATION OF GLASS PLATES AT DIFFERENT
TEMPERATURES, (RADIATION OF LAMPBLACK = 100),
Temp, of Lo-
Temp, of lu-
38. Let us call the proportional radiation of the glass plate
at 100 C unity, and we derive the following table.
PROPORTIONAL RADIATION OF GLASS PLATES AT DIFFERENT
TEMPERATURES, THEIR RESPECTIVE PROPORTIONAL RADI-
ATIONS AT 100 C. BEING RECKONED UNITY.
Temp, of In-
Temp, of Lo-
39. We see thus that the radiation of thick plates of glass in-
creases most rapidly, and that of thin plates least rapidly, as the
temperature increases, and we may suppose, that if we could
procure a plate of glass of sufficient tenuity, we might (without
heating the plate at all), by finding its absorption for heat of
RADIATION AND ABSORPTION.
different temperatures find its radiation at those temperatures,
which (if the plate were thin enough) would give us the law of
radiation of a glass particle. This law would not increase nearly
so fast with increasing temperatures asDulong and Petit's law ;
it may even be that the radiation of glass particles is propor-
tional to its absolute temperature.
40. But all substances (with the exception of black mica
and black glass, whose peculiarity may perhaps be otherwise ex-
plained) have the same properties as glass with regard to heat ;
that is, they are more diathermanous for heat of high than for
heat of low temperatures. The radiation of thin plates or
particles of all substances will therefore increase less rapidly
with temperature than that of black surfaces. It may there-
fore be, that the same law of radiation is common to very thin
plates or particles of all bodies ; this law (whatever it be) giving
in all cases, a less rapid increase of radiation with temperature
than is indicated by Dulong and Petit's law. Had, however,
the diathermancy of thin plates of different substances in some
cases diminished and in others increased for heat of high
temperature, the law of radiation of a particle could not have
been the same for all bodies.
The generality of this law of increased diathermancy of all
bodies for heat of high temperatures seems, therefore, to me,
to argue in favor of the universality of the unknown law of
particle radiation which depends upon the former.
41. What, then, does Dulong and Petit's law express ?
The answer is, it expresses the law of radiation of indefinitely
thick plates, and we have shown that it increases faster than
the law of radiation of a material particle.
To facilitate the comprehension of this subject as much as
possible, I have put it in the following shape. Suppose we
have two substances opposite one another, the one having the
temperature of 0, and the other of 100, the latter will of
course lose heat to the former let us call its velocity 100.
Suppose, now, that (the first surface still retaining its tempera-
ture of 0) the second has acquired the temperature of 400 ;
then we should naturally expect the velocity of cooling to be
denoted by 400 ; but by Dulong and Petit's law, it is much
greater. The reason of the increase may be thus explained.
At the temperature of 100 we may suppose that only the ex-
terior row of particles of the body supplied the radiation, the
heat from the interior particles being all stopped by the ex-
terior ones as the substance is very opaque for heat of 100 ;
while at 400 we may imagine that part of the heat from the
exterior particles is allowed to pass, thereby swelling up the
total radiation to that which it is by Dtilong and Petit's law.
42. We have thus ascertained 1st, That Dulong and
Petit's law is not the law of radiation of a material particle ;
and, 2d, That this law increases less rapidly with the tempera-
ture than Dulong and Petit's law. But now the question arises,
can any method be indicated of ascertaining, experimentally
the law of radiation of a material particle ? Now, by con-
tinually diminishing the thickness of the plate whose radiation
at different temperatures we are ascertaining, we certainly ap-
proach nearer and nearer to the desired law, and, by using the
method indicated in Art. 37, we may avoid heating this plate
at all and thus overcome one source of experimental difficulty.
Yet the thinnest plate we can procure of a substance such as
glass or mica acts, to all intents, as an indefinitely thick sub-
stance for a great many of the rays of heat that is, it stops
them all. The change, therefore, of the unknown law of par-
ticle radiation into Dulong and Petit's law will to a great
extent, have taken place even within this very thin plate ; so
that, in order to reach the desired law or even approximate to
it, we should have to use much thinner plates than we could pos-
sibly procure ; and, even without the necessity of heating the
films, the experimental difficulty and labor of such an investi-
gation would be very great.
On the other hand, we may suppose that, since a thin film
stops so much heat, a portion may be stopped in the physical
surface of the body, and the absorption might thus influence
the law of reflection of heat from the surface. The amount
of this influence depending on the absorptive nature of
the particles, we might be able to measure the absorption, and,
consequently, the radiation of the physical surface, that is, of
a very thin plate. But, in the first place, the difficulties of
such an investigation would be even greater than in the previ-
E A D I A T I N A N D A B S R P T I N .
ous case ; and, in the second place, the true law of reflection is
not yet finally settled.
I am therefore induced to think that it is nearly hopeless to
attempt to ascertain the true law of radiation of a material
particle, at least by any method of experimenting depending
upon the use of thin plates, or on the change which absorption
may be presumed to cause in the amount of heat reflected from
the surface of a body.
Edinburgh, March 22, 1859.
On General Diathermancy (added 15th June).
43. Circumstances having occurred which may interfere in
the meantime with my further experiments on heat, I annex
to this paper an account of some experiments made since the
day of reading. These were proposed with the view of ascer-
taining whether diathermancy is confined to rock salt or
whether bodies partake of this property. If the latter be the
case, the reason why we have not hitherto ascertained it to be
so is evidently the difficulty of obtaining crystals of many bodies
sufficiently large to operate upon ; and if we wish to prove these
diathermanous we must do so in a way that does not render nec-
essary the use of large crystals.
44. Now, a body that is transparent for light, forms, when
pounded, a white powder or one that reflects a great deal of
light. It will be granted that the reason of this is because we
have not only the reflection from the outer surfaces of the
crystals, but also from many interior surfaces. Now the same
remark is applicable to heat. A body that is diathermanous or
transparent for heat should, as a powder, be white for heat, or,
in other words, reflect it. But (First Series, Art. 31) the re-
flection plus the radiation of the body at any temperature
equals the lampblack radiation at that temperature. Hence a
powdered diathermanous substance ought to radiate less than
lampblack. Accordingly, different substances having been
pounded into a fine crystalline powder, made into a paste with
water, spread on the two sides of parallelopipedons of wood,
dried and one of the sides, when dry, rubbed over with lamp-
black, the following result was obtained :
NAME OF SUBSTANCE.
Sulphate of potash
Nitrate of potash . .
45. Tims we see that table salt being white for heat, the
radiation of the white side is less than that of the black side ;
and further, white sugar and alum being both nearly black for
heat, the radiation of the one side is nearly equal to that of
the other. We see, moreover, that sulphate of potash and
nitrate of potash, especially the latter, are white for heat, al-
though not quite so much so as table salt. May we not there-
fore presume that these substances are diathermanous ? There
is, moreover, the following method of confirming the testi-
mony in favor of the diathermancy of these substances as
derived from this experiment.
46. Table salt being white for heat, part of the reflected
heat will be composed of rays which have been reflected
from the internal surfaces of crystals. Such rays have there-
fore been sifted, having left behind that description of heat
which passes with difficulty through rock salt and also (Art.
9) through mica. The whole reflected heat from a surface of
table salt should therefore be of a nature which passes more
easily through mica than ordinary heat, and (First Series,
Arts. 31 and 33) since the sum of the reflected and the radi-
ated heat is equal both in quantity and quality to that from
lampblack, it follows that the radiated heat from table salt
(and probably from other substances white for heat) should, in
order to make up the average quality, have a somewhat greater
difficulty in passing through mica than ordinary lampblack
heat. Accordingly, it was found that the diathermancy of a
mica screen for heat from table salt was less than that for or-
dinary lampblack heat in the proportion of 92 to 100, while
it was less for heat from pounded sulphate of potash in the pro-
portion of 93 to 100, thus confirming the analogy between
RADIATION AND ABSORPTION.
rock salt and sulphate of potash. No such difference was ob-
served for heat from sugar.
47. We see also from the above table that the radiation and
therefore the absorption of table salt is 83.1 per cent, leav-
ing 16.9 per cent for the reflected heat. Now Melloni found
that chalk absorbed 56.6 per cent, and consequently reflected
43.4 percent, of heat from a Locatelli lamp; and if we sup-
pose table salt to be at least as white as chalk for heat of that
temperature, we must conclude that table salt is less white for
heat of 212, than for heat from a Locatelli lamp, following in
this respect the same law as chalk, which, from being nearly
black for heat at 212, becomes comparatively white for heat
from a Locatelli lamp. There is also little doubt that table
salt reflects more than 16.9 per cent of the light that falls upon
it. Hence we may conclude generally that powders even of
diathermanous bodies are less white for heat of low tempera-
ture than for heat of high temperature and for light.
48. It would also seem, that, although comparing one
powder with another, there is no relation between apparent
whiteness and whiteness for heat, since it was found that very
white surfaces of pounded sugar and alum (the particles com-
pressed, not made into a paste with water) reflected little or no
heat ; yet, comparing powdered surfaces of the same diather-
manous body together, there seems to be some relation between
their apparent whiteness and their whiteness for heat, in-
sufficient pounding, or any circumstance which diminishes the
apparent whiteness, diminishing also its whiteness for heat.
MEMOIRS ON RADIATION AND ABSORPTION.
BALFOUR STEWART was born Nov. 1, 1828 at Edinburgh.
He studied at the Universities of St. Andrews and Edinburgh,
and later entered upon commercial life. His particular taste
for physical science soon developed itself, however, and we have
in 1858 a couple of his earliest papers. He became associated
with Kelland and Forbes at this time and in 1858 contributed
his most important work on the extension of Prevost's Theory
of Exchanges in radiation. With the elaborate (at that time)
facilities at his command he was able to demonstrate the equal-
ity of the radiating and absorbing power of every substance.
For this and other work he was awarded the Rom ford Medal
some years later. In 1859 he was appointed director of the
Kew Observatory, where for eleven years he directed the im-
portant studies and investigations carried on there. During
this period he was seriously injured in an accident from which
he never recovered. In 1870 he was appointed to the chair
of Physics in Owens College, Manchester, which he occupied
until his death Dec. 19, 1887. During this time he issued
his well-known texts in Physics. His " Conservation of
Energy," " The Unseen Universe" (in conjunction with Tait),
his experiments on the viscosity of ether, etc., all illustrate the
comprehensiveness of his mind and the originality of his
ON THE RELATION BETWEEN THE
EMISSIVE AND THE ABSORPTIVE
POWER OP BODIES FOR
HEAT AND LIGHT.
G. R. KIRCHHOFF.
Reprinted from " Investigations on the Solar Spectrum and
the Spectra of the Chemical Elements," 2d. Edition, Berlin,
Ferd. Dummler's Publishing House, 1866, Gesammelte Abhand-
lungen, pp. 571-598, Leipzig, 1882.
Nature of Heat Rays and Light Rays . . . . 75
#/#6'& Bodies defined . . . . . . . . 76
Definitions . . -. . . . .. . . . 77
Ratio between the Emissive and the Absorptive Poiver . 78
Proof of the Law of Emission and Absorption for Black
Bodies .: 78
Proof of the Law of Emission and bAsorption for Any
Body , . 89
Generalization of the Law of Emission and Absorption . 92
Some Results of the Law , . ' . ' . . . 94
ON THE RELATION BETWEEN THE
EMISSIVE AND THE ABSORPTIVE
POWER OP BODIES FOR
HEAT AND LIGHT.'
HEAT rays have the same nature as light rays ; these con-
stitute a special class of the former. The invisible heat rays
are distinguished from light rays only by the period of vibra-
tion or the wave length. All heat rays follow the same laws
in their propagation, which are known for light rays. A
luminous body in space sends out light rays that are indepen-
dent of the bodies on which they fall ; similarly all heat rays
which a body sends out are independent of the bodies which
form its environment.
Of the heat rays that are sent out to a body by its surround-
ings a part are absorbed, the others are sent on in directions
which are varied by reflection and refraction. The rays re-
fracted and reflected by it pass off along with those sent out by
it, without any mutual disturbance taking place.
Through the radiations which a body sends out, the quantity
of heat which it contains will, according to the law, sustain a
loss which is equivalent to the vis viva of those rays and,
through the heat rays which it absorbs, a gain which is equiv-
alent to the vis viva of the absorbed rays. But in certain cases
an exception to this rule may occur, in that the absorption and
the radiation produce other changes in the body, as for ex-
ample in bodies which are chemically changed by light, and
light absorbing media which lose their power of shining
1 Investigations on the solar spectrum and the spectra of the chem-
ical elements, 2d. Edition, Berlin, Ferd. Dummler's publishing house
through the radiation of the light which they have absorbed.
Such cases should be excluded on the assumption that neither by
means of the rays which it radiates or absorbs, nor by means of
other influences to which it is exposed, does the body possess the
power to undergo a change, if its temperature is kept constant by
the addition or the subtraction of heat. Under these conditions,
according to the law of equivalence of heat and work, the
amount of heat which must be transferred to a body in a given
time to prevent cooling, which would occur in consequence of
its radiation, is equivalent to the vis viva of the emitted rays ;
and the amount of heat which must be withdrawn in order to
counterbalance the heating from absorption of radiations, is
equivalent to the vis viva of the absorbed rays.
Let a body which satisfies these conditions be surrounded by
an enclosure, having the same temperature, through which no
heat rays can penetrate, whose temperature is kept constant
and which satisfies the same conditions. The body sends out
heat rays and is encountered by such heat rays, which, in part,
proceed from the enclosure, in part, are thrown back to the
same by reflection from it, absorbing a part of them. Its tem-
perature must thus remain the same, unless heat is withdrawn
from it or communicated to it as follows on the principle from
which Carnot's law results. For this reason, the vis viva of
the rays, which it sends out in a certain time, must equal the
vis viva of the rays which it absorbs in the same time.
The proof which rests upon this conclusion requires the ac-
curate investigation of the rays that travel back and forth be-
tween the body and the enclosure. This investigation will be
much simplified if we imagine the enclosure to be composed,
wholly or in great part, of bodies which, for infinitely small
thickness, completely absorb all rays which fall upon them.
I will call such bodies perfectly black, or more briefly black.
A black body, in this sense of the word, must have the same re-
fractive index as the medium in which the radiation takes
place ; then there will be no reflection at its surface, and all in-
cident rays will be wholly absorbed. Thick iodine vapour in
contact with air, or pitch in contact with glass, may be treated
as black bodies, approximately, but not iodine vapour in con-
tact with glass or pitch in contact with air. Next, the radia-
RADIATION AND ABSORPTION.
tion in empty space will be investigated ; the Mack bodies re-
ferred to must therefore have a refracted index which differs
only infinitely little from 1.
The assumption that such black bodies are conceivable forms
an important aid in the proof which will be presented here.
Further, it will be assumed that perfectly diathermanous
bodies are conceivable, that is, such which will absorb none of
the incident heat rays of whatever nature these may be, and
finally, that a perfect mirror is conceivable, i.e., a body which
reflects completely all heat rays. A perfect mirror, like every
diathermanous body, can itself send out no rays ; for if it did
(confined in an enclosure of like temperature) it would warm
this enclosure more and more and cool itself more and more.
Before a body C, Figure 1, imagine two screens, /Si and Sz placed
in which are two openings 1 and 2, whose dimensions are infi-
nitely small with respect to their distance
apart, and each of which has a center. s *
Through these openings passes a pencil
of rays sent out by the body C. Of this
pencil of rays, let us consider the part,
whose wave length lies between A and
/i-j-rJA, and let this be divided into two n
polarized components, whose planes of
polarization are the planes a and b per-
pendicular to each other, passing through
the axis of the ray pencil.
Let E&\ be the intensity of the com-
ponent polarized in a, or, what is the same thing, the increase,
which the vis viva of the ether beyond the screen S% experiences
through this component in the unit of time. The quantity
E is called the emissive power of the body C.
Conversely, upon the body C there falls through the open-
ings 2 and 1 a pencil of rays having the wave length A, polar-
ized in the plane a; of this, the body absorbs a part while it
reflects or transmits the remainder ; let the ratio of the inten-
sity of the absorbed rays to the incident rays be A and let this
be called the absorptive power of the body C. The quantities
^and A depend upon the nature of the condition of the body
6', besides also upon the form and position of the openings 1
and 2, the wave length A and the direction of the plane a.
Under these conditions the following law holds : The ratio be-
tween the emissive and the absorptive power is the same for all
bodies at the same temperature.
This law will be proven, first, for the case where only black
bodies are compared with each other, that is, those whose
absorptic power = 1 ; i. e., it will be shown that the radiating
power of all black bodies is the same at the same temperature.
The proof of this special law is similar to that of the general
law, but simpler ; it will therefore facilitate the understanding
of the latter. Moreover, conclusions which are drawn from
the special law will be used in the proof of the common law.
Proof of the Law 3 for Hack bodies.
Let (7 be a black body ; let its emissive power, which is com-
monly indicated by E, be called e ; it will be proven that e
remains unchanged, when C is replaced by any other black
body of the same temperature.
Imagine the body C' enclosed in a black covering, of which
the screen 82 forms a part, let the second screen 182, like the
first, be made of black substance and let both be united with
each other on all sides by black walls, as shown in Figure 2.
Suppose the opening 2 to be closed at first by a black surface,
which I will call surface 2. The whole system must have the
same temperature and the covering be maintained at a constant
temperature throughout. According to the statements made
in Figure 2, 1, the vis viva of the rays which the body C" sends
out in the given time, must then equal the vis viva of the rays,
which it absorbs in the same time ; in other words : the sum of
the intensities of the rays which it sends out must equal the sum
of the intensities of the rays which strike it, since according to
KADI AT ION AND ABSORPTION.
supposition it completely absorbs the latter. Now suppose the
surface 2 removed, and the opening closed by a portion of a
perfectly reflecting spherical surface, placed directly back of it
and having its center at the middle point of the opening 1.
Equilibrium of temperature will then exist. There must also
be equality between the intensity of the rays which the body C
sends out, and of those incident upon it. Since the body C
now sends out the same rays as in the cases
previously considered, it follows that the
intensities of the rays incident upon C are
the same in both cases. By the removal of
surface 2 the rays are withdrawn from C
which pass through opening 1 ; therefore
the concave mirror placed at opening 2
throws just the same rays back to C which
this sends out itself through the openings
1 and 2, for the concave mirror forms from
opening 1 an image which coincides with
The law given would therefore be proved
if all rays of the two pencils compared have the wave length
\ and are polarized in the plane a. Both pencils of rays,
however, are made up of different components and form the
equality of the intensity of the whole pencil. "We may not
directly infer the equality of the intensity of corresponding
The necessary completion of the proof may easily be given
when a plate is supposed to exist, having the property of trans-
mitting undiminished rays whose wave length lies between a
and A + <tt. and whose plane of polarization is parallel to the
plane a; but which completely reflects rays of other wave
1 The diffraction of the rays at the edges of opening 2 may he neg-
lected, since the openings 1 and 2 may be assumed infinitely small with
respect to their distance and yet infinitely great with respect to the
wave length, that is, so great, that the defraction may be inappreciable.
From this it follows that the intensity of the pencil of rays, which the
body C sends ont through openings 1 and 2, equals the intensity of the
pencil of rays which the black surface 2 sends out through the opening
1. Since this intensity is independent of the form and further character
of the black body C, so, likewise, is the former.
lengths or of an opposite polarization. If we should imagine
the arrangement shown in Figure 2 modified by bringing such
a plate before opening 1, then we may immediately arrive at
the law to be proved by the treatment employed in respect to
The assumption that such a plate is possible is in no wise
justified. On the contrary, a plate is possible which, of the
rays striking it at the same angle, transmits and reflects them
in different degrees according to their wave length and plane
of polarization. A plate, which is so thin that the colors of
thin films are visible and which is placed obliquely in the path,
Such a plate is required for the investigation under consid-
eration in order to compare them. Besides this, it is necessary
to make such an arrangement that both pencils of rays do not
pass through the plate, but are reflected from it at the polariz-
ing angle, the plane of reflection coinciding with the plane a.
This is advantageous in as much as the rays polarized perpen-
dicularly to a need not be considered. Further, the plate must
be made of a perfectly diathermanous medium, it will then
absorb no rays and send out none.
In the arrangement described in Figure 2 imagine a plate of
s 2 the kind described and designated as P,
brought between the openings 1 and 2 (Fig.
3). Let it be so placed that the pencil of
rays passing through the openings 1 and 2 is
incident at the polarizing angle and the
plane of incidence is the plane a. Let the
wall which unites the screens Si and 83 be
so shaped that the image, which the plate
P casts from the opening 2 lies within it ;
in the place and of the form of this image
imagine an opening which I will call open-
ing 3. Let opening 2 be closed by a black
surface of the temperature of the whole
system, and let opening 3 be closed in the first place by a
similar surface, and in the second place by a perfect concave
RADIATION AND ABSORPTION.
mirror having its center where the plate P forms the image of
the middle of opening 1. In both cases the equilibrium of
temperature is maintained ; through consideration given in
the preceding paragraph, it follows therefore that the sum of
the intensities of the rays, which the body C is deprived of
through the removal of surface 3 equals the sum of the inten-
sities of the rays which are brought to it through the agency
of the concave mirror. Let a black screen SB (of the temper-
ature of the whole system) be so placed that none of the
rays which surface 3 sends out are directly incident upon
opening 1. The first sum, then, is the intensity of the rays
which proceed from surface 3, and are reflected by plate P and
pass through opening 1; they will be designated by Q. The
second sum is made up of two parts ; one component comes
from C and is :
where r represents a quantity dependent upon the nature of
the plate P and the wave length A; the second part consists of
rays which have come from a portion of the black wall which
unites the screen S l and $ 2 ,have passed through the plate P
and been reflected from the concave mirror, and then from the
plate P; this part will be designated as R. It is unnecessary
to examine further the value of R; it suffices to notice that R,
as well as Q, is independent of the nature of C. Between the
magnitudes introduced there exists the equation :
:/eV 2 -f- R = Q
If we now imagine the body C replaced by another black
body of the same temperature, letting e indicate for this what
e has represented for the other, there exists the equation
<T/e'r 2 -f E = Q
From this it follows that
dl. (ee') r' 2 =
Let us now assume that the index of refraction of the plate P
differs but little from unity. From the theory of the colors of
thin plates it follows then that we can place
r = p sin 2 -?-
where p represents a quantity proportional to the thickness of
the plate P, independent of A, and a quantity independent of
this thickness. From this follows the deduced equation :
' Since this equation must hold for every thickness of the
plate P> and hence for every value of p, it follows that for
every value A we may conclude that
To prove this, substitute in that equation for sin* ~- :
i(cos4 ~ 4 cos 2 ~ _i_Q)
A A ' '
and differentiate twice with respect to p : we then have
4 -f- cos 2 f- ) =
In place of A let us introduce a new quantity into the equa-
tion ; where
we thus obtain
daf (a) (cos 2 p a cos p a) =0
If we consider that when (a) represents any arbitrary func-
tion of a
J /* a
da? (a) cos 2 pa = I da<j> ( -~- ) cos pa
o *J o
from which we may conclude that if we substitute for c , we
may therefore write
d* \f( g- ) 2/ (a)] cos p a =
RADIATION AND ABSORPTION.
Multiply this equation by dp cos xp, where x represents an arbi-
trary quantity, and integrate it from p = to p = oo. Accord-
ing to Fourier's formula which is expressed by the equation
/* C** TT
I dpcospx I da^ (a) cos pa = $ ( x )
Jo Jo 2
OP /(-I. ) = 2/(a)
From this it follows that /(a) either vanishes for all values
of a, or becomes infinitely great when a approaches zero. When
a approaches zero A becomes infinite. If we remember the
meaning of /(a) and consider that p is a proper fraction, and
that neither e nor e' can become infinite when A increases to
infinity, then it is evident that the second case cannot exist
and therefore, that for all values of A, e = e'.
In a similar way we may treat the case when C is not a black
body but is an arbitrary one. We shall not assume for the
same that it is homogeneous ; partly on its surface, partly in its
interior will the rays therefore, which are incident upon it from
the black envelope, experience the most manifold modifications.
On these grounds, there must be, as a preliminary to the pro-
posed proof, a study made of the radiation which takes place
between black surfaces of the same temperature, for arbitrary
bodies. To this investigation, which depends upon the formula
just proved, the following paragraphs are devoted.
MUTUAL RADIATIONS OF BLACK SURFACES.
If the pencil of rays which the body C sends out through
openings 1 and 2 should be partly linearly polarized, the plane
of polarization of the polarized portion must rotate when C is
rotated around the axis of the pencil. Such a rotation must
therefore change the value of e. Since, according to the equa-
tion proved, such a change cannot take place, the pencil of
rays can have no linearly polarized portion. It can be proved
also, that it can have no circularly polarized part. But the
proof for this will not be given here.
We will also grant, without this, that black bodies are con-
ceivable in whose structure there is no reason why they should
send out in any direction more right handed circularly polarized
rays than left handed circularly polarized rays.
Of this character will the black bodies, concerned in the fur-
ther treatment, be assumed ; they send out in all directions
The quantity represented by e depends, aside from the tem-
perature and wave length, on the form and the relative position
of the openings 1 and 2. If w\, w? represent the projections of
the openings upon planes perpendicular to the axis of the pen-
cil, and if s is called the distance of the openings, then
where /is a function of the wave length of the temperature
Since the form of a body C is arbitrary, a surface may be
substituted, which exactly fills opening 1 and which I will call
surface 1 ; the screen Si may then be imagined removed. Fur-
ther the screen $2 may be considered removed if the pencils of
rays which e covers, is defined as that which falls from surface
1 upon surface 2, which the opening 2 exactly fills.
A consequence of the last equation, which immediately fol-
lows and which will later be used, is that the value e remains
unchanged if we imagine the openings 1 and 2 interchanged.
We will now establish a law which may be treated as a gen-
eralization of the law presented in the last paragraph.
Between the two black surfaces of the same temperature 1
and 2, is placed a body which may refract, reflect, or absorb in
any way the rays which one sends to the other. Several pencils
of rays may pass from surface 1 to surface 2 ; choose one of
these, and consider the part of the one at 1 whose wave length
lies between A and A -f eZ/i, and divide this into two components
RADIATION AND ABSORPTION,
whose planes of polarization are the planes of a\ and b\ which
are perpendicular to each other (otherwise arbitrary). Let the
part of the first component which enters 2 be divided into two
components whose planes of polarization are the planes a 2 and
b 2 perpendicular to each other (otherwise arbitrary). Let the
intensity of the component polarized in 2 be Kd'k. Of the
pencil of rays which passes over the same path as the preceding
one, from 2 to 1, let us consider the part at 2 whose wave
length lies between A and a + dA, and divide this into two com-
ponents polarized in # 2 and Z> 2 . Divide the portion, which
reaches 1 from the first component, into two parts whose planes
of polarization are a\ and b\. Let the intensity of the com-
ponents polarized in a\ be K'd'\. Then
The proof of this law will be made upon the assumption that
the rays under consideration undergo no weakening in their
path, and also upon the assumption that refraction and reflec-
tion occur without loss, that there is no absorption and that
the rays, coming from 1, polarized in a\, reach 2 polarized in 2 ,
and vice versa.
Through the middle point of 1 pass a plane perpendicular to
the axis of the pencil of rays, either incident or emergent at
this point, and imagine in this a right-angled coordinate sys-
tem, whose origin is that middle point. Let
x\ y\ be coordinates of any point in the plane,
Figure 4. At the distance of unity from this
plane, imagine a second, parallel to it, and iu
this, a coordinate system whose axes are parallel
to each of those, and whose origin lies in the
axis of the pencil of rays. Let Xs y$ be coordi-
nates of any point in this plane. In a similar
FIG. 4. manner pass through the middle point of 2, a
plane perpendicular to the axis of the bundle of rays, incident
or emergent at this point, and introduce in this, a rectangular
system of coordinates whose origin is the middle point men-
tioned. Let x 2 y<2 be coordinates of a point in this plane.
Finally, at a distance of unity from this plane and parallel to
it imagine a fourth, and in it a system of coordinates whose
axes are parallel to the axis of x*, y? and whose origin lies in
the axis of the pencil of rays. Let x, y be coordinates of any
point in this fourth plane.
From an arbitrary point let a ray pass to any other point
(#2, #2) ; let Tb& the time required to pass from one point to
the other ; we will suppose it to be a known function of x\, y\,
#2, y<2> If the points (x 3 , y 3 ) and (x, y*) He in the path of the
ray referred to, (and if for the sake of brevity the velocity of
the ray in vacua be taken as unity) the time which the ray re-
quires to pass from (x 3 , y 3 ) to (z 4 , y*) will be
Assuming the points (#3, 2/3), (#4, y 4 ) given, and the points
(a?i, y\), (#2 #2) required, we could find these from the condition
that the above expression is a minimum. If we assume that
the eight coordinates x\, y\, x 2 , y 2 , x 3 , yz, x, y are infinitely
small, the following equations express the condition that the
four points (x\, #1), (z 2 , 2/2), (#3, #3), (x, ?/ 4 ) lie in one ray :
dx l ' dx 2
Now let (xi,yi) be a point in the projection of surface 1 on the
plane Xi, y\ and let dx\ 9 dy\ be an element of this projection in
Ayjiich the point Xi, y\ lies and which is infinitely small with
respect to the surfaces 1 and 2. Let (x 3 , y 3 ) be a point in a
ray proceeding from (x\, y\) to surface 2, dx 3 , dijs, a surface
element in which the point (x 3 , y 3 ) lies, of the same order as
dx\, dy\. The intensity of the rays of the required wave
length and of the given plane of polarization, which, proceed-
ing from dx\, dy\, pass through dx 3 , dy 3 , is then according
d\ I dx\ dy\ dx 3 dy 3 .
According to the supposition, this amount of rays reaches
surface 2 undiminished and forms an element of u quantity des-
ignated by Kdh. JTis the definite integral
RADIATION AND ABSOKPTiON.
/ f f f f
\s \s \s */
The integration here with respect to x%, ?/ 3 is to be taken
over those values which these quantities have according to the
above equations, while x\ and y\ remain constant and x 2 ,i/2 have
all the values which correspond to the projections of surface 2
upon the plane # 2 , y 2 . The integration with respect to x\, y\
is then to be taken over the projection of surface 1. The
dx 3 dys so limited,
/* /* /
or from the equations for z 3 , f/ 3
C r / ^' 2y t) 2 r ^ 2 r _ __
/ / \^Xj fix 2 by i by 2 '^ '*'" ' x/> / * / " * ^^'
where the integration is taken over the projections of surface 2
C C C/ tfT fPT ^T tfT \
)dxidyi dx 2 dy%
where the integration is taken over the projections of surfaces
1 and 2.
If the magnitude of a K' be treated in the same way, remem-
bering that a ray requires the same time to pass over a path be-
tween two points in either direction, the same expression
will be found for K' as for K. Thus, the enunciated law is
proved, subject to the limiting conditions under which it will
next be proved. This limitation may, however, be immediately
disposed of by an observation made by Helmholtz in his
"Physiological Optics," p. 169. Helmholtz says here (with
somewhat different notation) : " A light ray passes from point
1 to point 2 after any number of refractions, reflections, etc.
Through 1 suppose two arbitrary planes a\ and #1 passed in the
direction of the ray perpendicular to each other, in which its
vibrations are supposed to be resolved. Two similar planes, 2
and #2 are also passed through the ray at 2. Then the following
may be proved : If a quantity i of light polarized in the
plane a\ proceeds from 1 in the direction of the ray mentioned
and of this, the quantity k of light polarized in the plane a\
reaches 2, so will vice versa the quantity k of light polarized in
# 2 reach point 1 if the quantity i of light polarized in a 2
proceed from point 2." 1
Applying this law, and representing by 7 the value of the
ratio 4 for the two rays which pass in either direction between
the points (x\, y\) and (# 2 , 3/2), then an expression is obtained for
K &s well as for K which differs from that formed only in that
now y appears as a factor under the integral sign.
The equality of ./Tand 7T' exists accordingly when > has a
different value for the rays into which one of the pencils com-
pared may be divided ; for example, it is unaffected if a part of
the pencil is intercepted by a screen.
Of the same pencils which were compared in the preceding
paragraphs, the following law also holds : of the pencil passing
from 1 to 2, consider the part at 2 whose wave lengths lie be-
tween A and A + dl and resolve this into two components polar-
ized in 2 and #2 ; let the intensity of the first component be
Hd'k. Of the pencil which passes from 2 to 1, consider at 2 the
portion whose wave lengths lie between A and A + d% 9 and resolved
this into two components polarized in a 2 and Z 2 . Let the por-
tion of the first component reaching point 1 be H'd\.
Then H=ff'. The proof of this law is the following ;
^and K are to have the same meaning as in the preceding
paragraph ; let L and L' be the quantities which arise form K
and K'. when plane a\ is interchanged with plane bi.
1 The law of Helraholtz, as he himself noted, does not hold good
when the plane of polarization of a ray undergoes any rotation, such as
magnetic force produces according to Faraday's discovery ; therefore,
in the following considerations magnetic force must not be considered
as present. Helmholtz limited his law also by supposition that light
undergoes no change of refrangibility such as occurs in fluorescence ;
this limitation is unnecessary in the application of the law, if rays of
only a given wave length are regarded.
RADIATION AND ABSORPTION.
Then L = L' } similarly K = K', further H K+ L, because
rays polarized perpendicularly to each other do not interfere,
when they are brought back to a common plane of polarization
in case they are a part of an unpolarized ray ; and according to
6 the surface 1 sends out unpolarized rays.
Finally H' = K+ L', because two rays, whose planes of polar-
ization are perpendicular to each other, do not interfere.
From these equations it follows that H= H'.
Let Fig. 2 have the same meaning as in 4, only let the body
C be not a black body but an arbitrary one. Let opening 2 be
closed by surface 2. This surface sends out a pencil of rays
through opening 1 to the body C, which is partly absorbed by
this body, and partly scattered in different directions by reflec-
tion and refraction. Of this pencil consider the part between
1 and 2 whose wave lengths lie between A and A + d\ and resolve
this into two components polarized in plane a and the plane
perpendicular to this. Let that part of the first component
which escapes absorption by C, and hence strikes the black cov-
ering in which the body C is inclosed, be M'd"k. A certain por-
tion of the rays which a part of the covering sends out to the
body C, fall upon surface 2 through opening 1 ; thus by means
of the body C a pencil of rays is produced which passes through
opening 1 to the surface 2. Of this, consider the part whose
wave lengths lie between A and A + dh and divide it into two
components polarized in plane a and the plane perpendicular
to it. Let the intensity of the first components be Md\.
Then M= M '. The truth of this law follows from the propo-
sition from the preceding paragraph, if we apply this to all
pencils of rays, which surface 2 and all the elements of the
black cover surrounding the body C interchange with each
other by means of the body C, and then form the sum of the
equations so obtained.
Proof of the proposition # for any body.
Let the arrangement shown in Fig. 3 and described in 5 be
MEM OIKS ON
taken, only let the body C no longer be a black body, but ar-
bitrary. Ill both cases described there, the equilibrium of heat
subsists ; then the vis viva which is drawn out from the body
G by the removal of the black surface 3, must therefore be
equal to the vis viva which is supplied to this by the presence
of the concave mirror. The symbols used in 5 will be used
here with the same meaning. The letters E and A will have
the meaning given them in 2.
If surface 3 is removed, then the rays are withdrawn from
the body C which this surface sends to it ; the intensity of the
part of these rays which it absorbed is = f cUer A.
Now the rays must be examined which are transmitted to
the body by the presence of the concave mirror. All these rays
must be reflected from the concave mirror to plate P and from
this to opening 1, and these must pass in the same direction as
if they came from opening 2. Before they strike the concave
mirror, they have either experienced a reflection from it or not.
In the first case they can only be sent back again to the con-
cave mirror by means of the body (7 over the path which is the
reverse of that already described. It must next be premised that
the body (7 has such a position that, of the rays which pass to
it through 2 and 1, only an infinitely small part will be re-
flected back again through opening 1 to opening 2. Then, of the
rays in question, only an infinitely small fraction have suffered
multiple reflection at the concave mirror, audit is sufficient to
consider those which are reflected only once at the mirror. Of
these, a part proceed from the body (7, the rest from the black
covering. The first part has experienced a double reflection at
plate P ; the vis viva which the body absorbs from it is
The second part which proceeds from the black enclosure
may again be considered as consisting of two parts ; one which
passes to the concave mirror without the mediation of the body
C., and a second, by means of it. Each arises from rays which
proceed from black partition opposite the concave mirror,
and have passed through the. plate P, have been reflected from
the concave mirror to the plate P and from this to opening 1.
RADIATION AND ABSORPTION.
Without examining from which part of the black wall these
rays have proceeded, their intensity may be found by the law
established in 11.
By the application of this, the intensity of those rays which
were absorbed by the body C is shown to be
(/ACT (1 r)A.
Finally in order to find the intensity of the rays which proceed
from the black covering by means of the body C to the concave
mirror, and pass back from this to the body C and are here
absorbed, let N designate the quantity which the quantity in-
dicated by M in 12 becomes in consequence of plate P being
brought into its place and the surface 3 removed ; the intensity
is then = f MNr* A.
The difference between M and N arises only from .the varia-
tion which the rays, falling upon the body C from the black
covering through opening 1, undergo by the introduction of
plate P and the removal of surface 3. Suppose the plate P
brought into its position, without removing surface 3, then M
can undergo no change, since all the pencils of rays, which go
to the opening 1 remain unchanged ; the pencil proceeding
from surface 2, for example, suffers a loss through reflection at
plate P which will be exactly replaced by the reflection of the
rays going out from the surface 3. The difference MN is
therefore only produced by the removal of surface 3 and is also
equal to the part of M which arises from the rays sent out by
surface 3 to opening 1 by means of plate P. According to the
supposition made in these paragraphs concerning the position
of the body C, MNis infinitely small in comparison with the
intensity of the rays of equal wave length which surface 3
sends to opening 1 by means of plate P, as well as infinitely
small in comparison with the intensity of rays of equal wave
length and polarized in the plane a, which surface 2 sends to
opening 1 by the absence of the plate P, and therefore finite
and also infinitely small with respect to the quantity repre-
sented by M ' in 12 (assuming that 1 A is not infinitely
small). Since, however, as already pointed in the places cited,
M' = M , we may also place
But according to the definition given of M'
M' = e (1 A) and therefore
dA Nf 2 A = I eZ/e ( 1^ ) r 2 A.
o y o
The proposition presented at the beginning of this paragraph
would then be expressed by the equation :
JOO x00 sCO x00
o */ o */ o */ o
or by the equation f ^ (EAe) Af 2 = 0.
By the same treatment employed in 5 with reference to a
similar equation, we may conclude that for every value of A*
or substituting for e its value in 7.
E_ _ j Wi W%
A = 82 *
Thus, the law 3 is proved under the assumption that, of the
pencil which falls from surface 2 through the opening 1 upon
the body (7, no finite part is reflected by this back to the
surface^ ; further, that the law holds without this limitation,
if we consider that when the condition is not fulfilled, it is
only necessary to turn the body C infinitely little in order to
satisfy it, and that by such a rotation the quantities ^and A
undergo only and infinitely small change.
A Generalization of tlie Laiv 3.
The discussions given assume that the space in which the
radiation occurs is a vacuum. But the same treatment also
obtains when this space is filled with any perfectly diather-
manous medium ; only the function / will then be different
than in the former case. The symbol /may then be retained
for a vacuum and /' may be called the corresponding function
of temperature and wave length for a certain diathermanous
medium ; if n is the index of refraction of the same for the
RADIATION AND ABSORPTION.
temperature and wave length to which / and /' refer, then a
simple relation exists between I', I, and n ; the same follows
from the law already demonstrated as will be here shown.
Imagine a layer of a diathermanous medium bounded by two
parallel planes, and with one side in contact with the black sur-
face F. Let the thickness of the layer= 1. For this body, the
s , absorptive power of A , and the emis-
sive power E, in relation to a certain
pencil of rays will be investigated.
The opening 1 and 2 which determine
the form of the pencil will be in
screens S\ and $ 2 , of which the first
covers the surface of the layer hither-
tofore supposed to be free, and the sec-
ond is parallel to it; let the line
FIG. 5. joining the middle points of the open-
ings be perpendicular to the screens. Of any pencil of rays
of a definite wave length and direction of polarization, which
passes from the opening 2 to the opening 1, a fraction will be
reflected at the latter which may be designated by p ; the rest
passes to the surface J^and is here completely absorbed ; there-
To find E, represent by x, y ; x\, y\ ; and # 2 , y<* the coordi-
nates of a point of the surface F, the opening 1, and the open-
ing 2, reckoned from those points which are found in the axis
of the pencil. If these points lie in a ray, then if s again rep-
resents the distance of the two openings,
must be a minimum with respect to x\ and y\ : i. e.,
x = Xl - x ^- x i y = yi y*-yi
ns > ns
if w\ and w 2 are the surfaces of the two openings, we find by a
treatment, which is given in a more general form in 10, the
intensity of the rays (polarized in a and of wave lengths be-
tween A and 7i + d%) which, falling from J^upon opening 1, in
part, pass to opening 2,
,v , .
Of these rays the fraction 1 p goes through the opening 1
and arrives at the opening 2.
Tims E- (1-,) T -2tf*-
If these values of E and A are substituted in the equation
then r =
Results of the Law 5.
When any given body a platinum wire for instance is
gradually heated, it emits, up to a certain temperature, only
rays whose wave lengths are greater than that of the visible
rays. At a certain temperature, rays of the wave length of the
extreme red begin to be visible ; as the temperature rises
higher and higher, rays of a shorter and shorter wave length
are added, so that for every temperature, rays of a corresponding
wave length come into existence, while the intensity of the
rays of greater wave lengths increase. If the law proven be
applied to this case, it will be seen that the function / for
any wave length vanishes for all temperature below that of a
certain temperature, depending on the wave length for higher
temperatures increases with the same. From this it follows,
when the same law is applied to other bodies, that all bodies,
whose temperature is gradually raised, begin to send out rays
of the same wave length at the same temperature, and begin to
glow with red rays at the same temperature, and at a higher
common temperature, yellow, and so on. The intensity of
rays of a certain wave length which different bodies send out at
the same temperatures may, however, be very different ; it is
proportional to the absorptive powers of bodies for rays of that
particular wave length. At the same temperature accordingly
metal glows more brightly than glass, and this more brightly
than a gas. A body that remains perfectly transparent at the
RADIATION AND ABSORPTION.
highest temperature would never become incandescent. Into
a ring of platinum wire of about 5mm diameter, I introduced
some phosphate of soda and heated it in the nonluminous flame
of the Bunsen burner. The salt melted and formed a fluid
lens and remained perfectly clear; but it emitted no light,
while the platinum ring in contact with it radiated the most
Draper 1 has drawn the conclusion from investigations that
all solid bodies begin to glow at the same temperature. From
his researches he lias, however, noted that certain bodies like
chalk, marble, fluor spar glow at a lower temperature than
they should according to this law; he called this luminosity
phosphorescence, and said it clearly differed from glowing, by
the color. But whatever name may be given to this luminos-
ity, it is in contradiction with law, 3, and a body which shows
it must therefore not satisfy the assumptions which were made
in the proof of the law, that, at a constant temperature, it must
remain unchanged ; phosphorescence is not purely an effect of
heat, and is not exclusively determined by the temperature,
but is produced by changes in the body ; if these changes
whether they are chemical or of another nature have ceased
then the phosphorescence must vanish.
From the law, 3, it follows that a body, which absorbs more
rays from one plane of polarization than from another, sends
out in the same ratio more rays from the first plane of polar-
ization than from the second. Consequently, as is known to
happen, a glowing opaque body having a smooth surface sends
out light in directions oblique to this surface which is
partially polarized perpendicularly to the plane passing
through the ray and the normal to the surface ; of the incident
rays, which are polarized perpendicularly to the plane of in-
cidence, the body reflects less, but also absorbs more than it
does of rays whose plane of polarization is the plane of in-
cidence. According to this law the state of polarization of the
rays sent out may easily be given if the law ot the reflection of
the incident rays is known.
1 Phil. Mag. XXX. p. 345 ; Berl. Ber. 1847.
MEMO in S ON
A tourmaline plate, cut parallel to the optic axis, absorbs,
at ordinary temperatures, moraof the rays which strike it nor-
mally, if the plane of polarization of these is parallel to the
axis than when it is perpendicular to it. Assuming that the
tourmaline plate retains this property when it is at a glowing
heat, it must give out rays in a direction normal to it, which
are partially polarized in the plane passing through the optic
axis and which is the plane perpendicular to that which is
called the plane of polarization of the tourmaline. 1 have
proved this striking deduction from theory by experiment and
it confirmed the same. The tourmaline plates employed with-
stood a considerable temperature, glowing for a long time in
the flame of the Bunsen burner without undergoing any per-
manent change; only after cooling did they appear dull at the
edges. The property of polarizing transmitted light was
retained even at an incandescence, although in a considerable
less degree than at a lower temperature. This appeared on
observing, through a double refracting prism, a platinum wire
made incandescent in the flame and placed behind a tourma-
line plate. The two images of the platinum wire were of un-
equal brightness, although the difference was much less than
when the tourmaline plate was outside of the flame. The
double refracting prism was then given the position in which
the difference of the intensities of the two images was a maxi-
mum ; suppose the upper image were the brighter ; then, after
removal of the platinum wire the two images of the tourmaline
plate were compared. The upper image was not strikingly,
but, unmistakably, darkerthan the other; both images appeared
exactly like to two similar incandescent bodies, of which the
upper had a less temperature than the lower one.
Still another result of the law established may, in conclusion,
be admitted here. When a space is surrounded by bodies of
the same temperature, and no rays can penetrate through these
bodies, every pencil in the interior of the space is so consti-
tuted, with respect to its quality and intensity, as if it pro-
ceeded from a perfectly black body of the same temperature,
and is therefore independent of the nature and form of the
RADIATION AND ABSORPTION.
bodies, and only determined by the temperature. The truth
of this statement is evident if we consider that a pencil of rays,
which has the same form, but the reverse direction to that
chosen, is completely absorbed by the infinite number of reflec-
tions which it successively experiences at the assumed bodies.
In the interior of an opaque glowing hollow body of given tem-
perature there is, consequently, always the same brightness
whatever its nature may be in other respects.
GUSTAV ROBERT KIRCHHOFE, the son of Counselor-at-law
Kirchhoff, was born March 12, 1824, at Kdnigsberg. He took
his degree of doctor of philosophy at the University in 1847.
The following year he became private-docent at the University
of Berlin. He early showed those rare mathematical faculties
which later distinguished him. As early as his eighteenth year
he decided upon physics as the branch to which he should
devote his life's work. By 1845 he had investigated electric
currents, and established the two so-called Kirchhoff's laws for
current conduction. Other important papers on electricity fol-
lowed in rapid order. In 1854 he was called to Breslau, where
he became associated with Bunsen. He went to Heidelberg in
1854 where Bunsen had preceded him. Here in his prime he
wrought and sought for twenty years, and in connection with
Bunsen achieved some of the most important discoveries in the
history of physical science. In 1875 he accepted, after twice
declining an invitation to the University, a call to the chair of
theoretical physics at Berlin where he became associated with
his former colleague von Helmholtz. Here he delivered for
eleven years (with serious interruption in the last two years) his
famous courses of lectures on theoretical physics. It is during
this period that we find the most brilliant aggregation at Berlin
of scholars in the faculty of mathematics and physics during
the century. His contributions extend over optics, heat, fluid,
motion, electricity, elasticity, etc., and all bear the imprint of
the great genius he was. He died unexpectedly Oct. 17, 1887,
after many months of disability. His papers and lectures
have been collected and edited and now form one of the endur
ing monuments in physical science.
CHEMICAL ANALYSIS BY SPECTRAL
G. KIRCHHOFF AND R. BUNSEN".
Poggendorf ',? A nnalen, Band 1 10, 1 860 ; Gesammelte Abliand-
lungen von G. Kirclilioff. pp. 598-625, 1882.
Methods of Purifying Salts 101
Apparatus described . . . . . . .103
Sodium . . . . . . . , . . 107
Lithium . . . 109
Potassium . . . . . . . . . .113
Strontium, . . 113
Calcium . . . . . . . . . .115
Advantage of Spectrum Analysis over other Methods . . 122
Law of Reversed Spectra ... . 123
CHEMICAL ANALYSIS BY SPECTRAL
IT is well known that many substances have the property
when they are brought into a flame of producing in the spec-
trum certain bright lines. We can found on these lines a
method of qualitative analysis which greatly enlarges the field
of chemical reactions and leads to the solution of problems
unsolved heretofore. We shall confine ourselves here only to
the extension of the method to the detection of the metals of
the alkalis and the alkali earth and to the illustration of their
value iii a series of examples.
The lines referred to show themselves the more plainly, the
higher the temperature and the weaker the natural illuminating
power of the flame. The gas lamp 2 described by one of us
gives a flame of very high temperature and very small luminosity;
this is consequently especially adapted to investigations on
those substances characterized by bright lines.
In Figure 1 the spectra are represented which the flames
referred to give when the salts, as pure as possible, of potassium,
sodium, lithium, strontium, calcium, and barium are vaporized
in it. The solar spectrum is annexed in order to facilitate the
The potassium compound used for the investigation was
obtained by heating chlorate of potassium which had been six to
eight times recrystallized beforehand.
The chloride of sodium was obtained by combining pure car-
bonate of sodium and hydrochloric acid and purifying the same
by repeated crystallization.
The lithium salt was purified by precipitating fourteen times
with carbonate of ammonium.
For the production of the calcium salt a specimen of marble
1 Kirchhoff and R. Bnnsen, Pogg. Ami. Vol. 110. 1860.
2 Bunsen, Fogg. Ann. Vol. 100 p. 85.
I 1 & & S % M
RADIATION AND ABSORPTION.
as pure as possible, and dissolved in hydrochloric acid, was
used. From this solution the carbonate of calcium was thrown
down by a fractional precipitation with carbonate of ammonium
in two portions, of which only the latter, precipitated in calcium
nitrate, was used. The calcium salt thus obtained we dissolved
several times in absolute alcohol and converted it finally into
the chloride by evaporating the alcohol and by precipitation
with carbonate of ammonium in hydrochloric acid.
In order to obtain the pure chloride of barium we extracted it
from the commercial salt by pulverizing and boiling repeatedly
in nearly absolute alcohol. The residue thus extracted and
freed from alcohol was dissolved in water and thrown down by
fractional precipitation in two portions, only the second being
dissolved in hydrochloric acid, and the barium chloride thus
obtained being further purified by repeated crystallizations.
In order to obtain chloride of strontium, as pure as possible,
the commercial salt was crystallized out from alcohol, and frac-
tionally precipitated in two portions with carbonate of ammon-
ium, the second part being dissolved in nitric acid and the ni-
trate freed from the last traces of calcium by pulverizing and
boiling with alcohol. From the product thus purified the chlo-
ride of strontium was obtained finally by precipitating with
carbonate of ammonium and dissolving the precipitate in
hydrochloric acid. All these purifications were made in plat-
inum vessels as far as it was possible.
Figure 2 represents the apparatus which we have used
mainly in the observation
of the spectra. A is a
box blackened on the in-
side the bottom of which
has the form of a trapez-
ium and rests on three
feet ; the two inclined
sides of the same form an
FIG 2 angle with one another of
about 58 and carry the
two small telescopes B and C. The ocular of the first is removed
and replaced by a plate in which is a slit formed of two brass
cheeks which are placed at the focus of the objective. The
lamp D is so placed before the slit that the mantle of the frame
is intersected by the axis of the tube B. Somewhat beneath
the point where the axis meets the mantle the end of a very fine
platinum wire bent into a small hook and carried by the holder
E passes into the same; on this hook is melted a globule of the
chloride previously dried. Between the objective of the tele-
scopes B and C is placed a hollow prism F with a reflecting
angle of 60 and filled with carbon disulphide. The prism
rests on a brass plate which can be rotated on a vertical axis.
This axis carries on its lower end the mirror G and above it
the arm //which serves as the handle to rotate the prism and
the mirror. A small telescope is adjusted before the mirror
which gives an image of a horizontal scale placed at a short dis-
tance. By rotating the prism we can cause to pass before the
vertical thread of the telescope C the entire spectrum of the
flame and bring every portion of the spectrum into coincidence
with this thread. To every reading made on the scale there
corresponds a particular portion of the spectrum. If the spec-
trum is very weak the cross hair of the telescope C is illumi-
nated by means of a lens which throws some of the rays from a
lamp through a small opening which is placed laterally in the
ocular of the telescope C.
The spectra in Fig. 1. obtained by means of the pure chlo-
ride above mentioned we have compared with those which we
obtained if we introduce the bromides, iodides, hyd rated oxides,
sulphates, and carbonates of the several metals into the follow-
into the flame of sulphur,
" " " " carbon disulphide,
" " " " aqueous alcohol,
" " non-luminous flame of coal gas,
" " flame of carbonic oxide,
" " " " hydrogen and
" " oxyhydrogen flame.
From these comprehensive and lengthy investigations whose
details we may be permitted to omit, it appears that the dif-
ference in the combinations in which the metals were used, the
multiplicity of the chemical processes in the several flames, and
the enormous differences of temperatures of the latter exert no
influence on the position of the spectral lines corresponding to the
RADIATION AND ABSORPTION.
How considerable the differences of temperature mentioned
are, is shown by the following treatment.
We may arrive at an approximation of temperature of a
flame by means of the equation t = -?~, in which t is the
temperature of the flame sought, g the weight of the substance
burning in oxygen, w the heat of combustion of the same, p the
weight and s the specific heat of one of the products of combus-
If we take as the heat of combustion
of sulphur as 2240 C
' carbon disulphide
' marsh gas
' carbonic oxide
and place according to Regnault the specific heat at constant
for sulphurous acid =0. 1553
" carbonic acid =0.2164
" nitrogen =0.2440
" aqueous vapor =0.4750
we find accordingly the temperature
of the sulphur flame 1820 C
' bisulphide of carbon flame.... 2195
' coal gas flame 1 2350
' carbonic oxide flame 2 3042
' hydrogen flame in air 3 3259
' oxyhydrogen flame 4 8061.
It appears that the same metal compound gives in one of
these flames a spectrum as much more intense as the tempera-
ture is higher. Of the compounds of these metals, those give
the greatest intensity in a flame which have the greatest
In order to obtain a further proof that each of the severally
mentioned metals always give the same bright lines in the
spectrum, we have compared the spectra referred to with those
1 Liebig's Ann. Vol. CXI. p. 258
8 Gasometric Methods by R. Bunsen. p. 254.
which an electric spark produces which passes between
electrodes made from these metals.
Small pieces of potassium, sodium, lithium, strontium, and
calcium were fastened on a fine platinum wire and so melted in
pairs within glass tubes that they were separated by a distance
of 1 to 2mm from one another the wires piercing the sides of
the tubes. Each of these tubes was placed before the slit of
the spectroscope ; by means of a Bnhmkorff's induction
apparatus, we caused electric sparks to pass between the metal
pieces mentioned and compared the spectrum of the same with
the spectrum of a gas flame in which the chloride of the cor-
responding metal was brought. The flame was placed behind
the glass tube. When the Ruhmkorff apparatus was thrown
alternately in and out of action it was easy to be convinced,
without any accurate measurement, that, in the brilliant spec-
trum of the spark, the bright lines of thespectrnmof the flame
were present undisplaced. In addition to these there appeared
other bright lines in the spark spectrum a part of which must
be attributed to the presence of foreign metals in the electrodes,
others to nitrogen which filled the tubes after the oxygen had
partly oxidized the electrodes. 1
It appears, accordingly, beyond a question that the bright
lines of the spectra indicated maybe considered as certain proof
of the presence of the metal in consideration. They can serve
as reactions by means of which this material may be detected
more certainly, and quickly and in smaller quantities than by
any other analytical method.
The spectra, represented, refer to the case when the slit is
wide enough so that only the most prominent of the dark lines
of the solar spectrum are visible, the magnifying power of the
observing telescope being small (about four-fold) and the
intensity of the light moderate. These conditions seem to us
1 In one investigation with strontium electrodes we used a tube filled
with hydrogen instead of nitrogen, and the stream of sparks was trans-
formed very soon into an arc, while the sides of the tuhe were covered
with a gray precipitate. On opening the tube nnder rock-oil it appeared
that the hydrogen had vanished and a vacuum existed. The gns
appears, therefore, at the enormous temperature of the electric spark, to
have dissociated the strontium oxide which had not been completely
removed from the surface of the metal.
RADIATION AND ABSORPTION.
most advantageous when it is necessary to carry out a chemical
analysis by spectral observations. The appearance of the
spectrum may under other conditions be quite different. If the
purity of the spectrum is increased, many of the lines appearing
as single, resolve themselves into several, the sodium line, for
example, into two ; if the intensity is increased new lines appear
in many of the spectra shown and the relation of the brightness
of the old ones becomes different. In general the brightness of
a darker line increases with greater luminosity more rapidly
than the brighter ones,but not so much that the former exceed
these. A clear example of this is given by the two lithium
lines. We have observed only one exception to this rule,
namely, with the line Ba ?, which, with low luminosity, is
barely visible while Zto^appears very distinct, and, with greater
luminosity, much brighter than the former. This fact appears
of importance, and we shall make a further study of the same.
We will now consider more closely the characteristics of the
several spectra, the knowledge of which is of importance from
a practical standpoint, and indicate the advantage which the
chemical analytical method founded upon it furnishes.
Of all the spectral reactions that of sodium is the most sen-
sitive. The yellow line Na a, the only one which is shown in
the sodium spectrum coincides with Fraunhofer's line D and is
characterized by its peculiarly sharp boundary and its extraor-
dinary brilliancy. If the temperature of the flame is very high
and the quantity of the substance used very great, traces of a
continuous spectrum are seen in the immediate neighborhood
of the line. Lines of other substances, in themselves very
weak, lying near it appear still weak and will, therefore, often
first be visible after the sodium reaction has begun to disappear.
In the oxygen, chlorine, iodine and bromine compounds in
sulphuric acid and carbonic acid the reaction is most evident.
But it is present also in the silicates, borates, phosphates and
other non -volatile salts.
Swani has already called attention to the minuteness ef the
1 Pogg. Arm. Vol. C, p. 311.
quantity of common salt which can produce the sodium line
The following investigation shows that chemistry produces
no single reaction which in the remotest degree can compare in
sensitiveness with this analytical spectral determination of
sodium. We detonized in one corner of the experiment room
which contained about 60 cubic meters of air and as far as
possible from our apparatus three milligrams of chlorate of
sodium with milk sugar while the non-luminous flame was
observed before the slit. After some minutes, the flame, becom-
ing gradually colored pale yellow, gave a strong sodium line,
which, after ten minutes, again completely vanished. From the
weight of the detonized salt and the air contained in the room
it is easy to calculate that in a unit weight of the latter not a
?oWr<rzrr>kh part of sodium smoke could have been suspended.
As the reaction can be readily observed in a second, and as, in
this time, according to the rate of flow and the composition
of the gases in the flame, onty about 50 ccm or 0.0647 grams of
air which contained less than ^otfoWoirth of sodium salt, reach
the state of incandescence in the flame, it follows that the eye
is capable of detecting less than ^ootrotfth f a milligram of
sodium salt with the greatest distinctness. With such a sen-
sibility of the reaction it is evident that only rarely is a sodium
reaction not visible in glowing atmospheric air. The earth is
covered over more than two-thirds of its surface with a solu-
tion of chloride of sodium, which, by the waves breaking into
foam, is transformed continually into spray; the particles of
sea-water, which reach the atmosphere in this way, evaporate
and leave behind them motes of salt which vary in magnitude,
but, as it appears, are rarely absent from the atmosphere, and,
perhaps, serve to supply the small organisms the salt which the
larger plants and animals secure from the ground. The
presence in the air of salt, easily shown by spectral analysis, is
yet of interest from another standpoint. If, as we yet can
scarcely doubt, there are catalytic influences which are the
cause of the miasmic spread of disease, it is possible that an
antiseptic substance, such as salt, even in vanishingly small
quantities, may indeed not be without definite influence upon
such processes in the air. From daily and long continued
RADIATION AND ABSORPTION.
spectrum observation it would be easy to learn whether the
variation in the intensity of the spectral line Ncta, produced by
the sodium combination in the air, is related in any degree to
the appearance and the spread of endemic diseases.
In the exceedingly delicate sodium reaction may also be
sought the reason why all bodies exposed to the air show the
sodium line after a time when heated in the flame, and why it
is possible with only a few compounds to eliminate the last
trace of the sodium line No, a by crystallizing it out ten or more
times from water which has come in contact with platinum
vessels only. A hair wire of platinum, which has been freed,
by heating, from every trace of sodium, shows the reaction
most vividly again, if it is exposed some hours to the air. Dust
which settles in the room from the air shows it in the same
degree, so that, for example, the slapping of a dusty book is
quite sufficient to produce at a distance of several spaces the
most brilliant flashes of the No, a line.
The incandescent vapors of the lithium compound give two
sharply defined lines, one a very weak yellow Li (3 and a red
brilliant line Li a. In certainty and delicacy this reaction ex-
ceeds all those known heretofore in analytical chemistry. It
approximates in sensibility that of the sodium reaction perhaps
because the eye is more sensitive for yellow rays than for re'd. On
detonizing nine milligrams of carbonate of lithium with a large
excess of milk sugar and potassium chlorate in the room which
contained about 60 cubic meters of air, the line became quite
evident. The eye can therefore in this way, as a calculation
similar to the one made above will show, perceive less than
T _j TFTTTT th of a milligram of carbonate of lithium with the
greatest distinctness. 0.05 grams of the same salt, detonized in
the way already mentioned, made it possible to observe the Li a
line in the air of the same room during more than an hour.
The oxygen, chlorine, iodine and bromine compounds are
most suitable for observing lithium. But the carbonate, sul-
phate, and even phosphate are almost as well suited for this
purpose. Minerals containing lithium, as triphyllin, triphan,
petalit, lepidolith, need only to be held in the flame in order
to give the line Li a with an intense lustre. In this way it is
possible to show the presence of lithium in many f eld -spars,
for example in orthoclase from Baveno. The line is seen only
momentarily immediately after the insertion of the specimen in
the flame. Thus mica from Altenberg and Penig indicates the
presence of lithium while on the contrary mica from Miask,
Ashaffenburg, Modum, Bengal, Pennsylvania, etc., is free from
lithium. When in naturally deposited silicates only a vanish-
ingly small quantity of lithium is present, it escapes immediate
observation. The test in such cases is then best made in the
following way: we digest and evaporate a small quantity of the
substance for examination with hydrofluoric acid or fluoride of
ammonium, moisten the remainder with sulphuric acid, and
dissolve the dry mass with absolute alcohol. The alcoholic
solution is then evaporated to dryness, again dissolved with
alcohol, and the fluid, thus obtained, evaporated in as shallow a
dish as possible. The product which remains can be easily
scraped together by means of an erasing knife and brought into
the flame on platinum wire, i^th of a milligram of the same is
usually quite sufficient for the experiment. Other compounds
than the silicates, in which we may wish to detect the least
traces of lithium, maybe transformed into sulphates by evapo-
ration with sulphuric acid or in any other way and then treated
By means of these experiments, the unanticipated conclusion
is readily drawn that lithium belongs to those substances which
are most widely distributed in nature. This is easily shown by
means of 40 cubic centimeters of sea-water which was collected
in the Atlantic ocean in latitude 41 41' and longitude 39 14'.
Ashes of Fucoids (kelp) which was driven on to the Scottish
coast from the Gulf Stream contained appreciable traces of it.
All orthoclase and quartz from the granite of the Oldenwald
which we have tested show a lithium content. A very pure
drinking water from a spring on the western granitic declivity
of the Neckar valley in Schlierbach near Heidelberg contained
lithium, while the spring rising in the red sandstone which
supplies the water pipes of this chemical laboratory was free
from it. Mineral water, in a litre of which lithium can
scarcely be detected by the ordinary analytical methods, shows
RADIATION AND ABSORPTION.
the Li a line frequently if we put a drop of the same into the
flame on a platinum wire. 1 All the ashes of woods in the Olden-
wald which grow on granite soil, as well as Russian and
other commercial potashes examined by us, contain lithium.
Neither, even, in the ashes of tobacco, vine leaves, vine-wood
and grapes,' 2 as well as in the ashes of crops which were culti-
vated in the Rhine plain near Waghausel, Deidesheim and
Heidelberg on non-granitic earth, was lithium lacking, nor in
the milk of the animals which were fed upon these crops. 3
It will be scarcely necessary to remark that a mixture of
volatile sodium and lithium salts shows, along with the reaction
of sodium, that of lithium with a scarcely less preceptible sharp-
ness and distinctness. The red line of the last appears still
quite distinct when a small bead containing the y^^th part of
lithium salts is introduced into the flame, where the eye,
unaided, perceives in the same, nothing more than yellow
light of sodium without any indication of red coloration. On
account of the greater volatility of lithium salts, the sodium
reaction lasts somewhat longer. When, therefore, it is desired
to detect very small traces of lithium along with sodium, the
bead for testing must be introduced into the flame whilst we
are observing through the telescope. We then often observe
the lithium line only for a few moments during the first
products of volatilization.
In the production of lithium compounds on a commercial
scale spectrum analysis is a means of inestimable value in the
selection of the raw material used and the determination of an
efficient method of manufacture. Thus for example, it is only
necessary to evaporate a drop of the different mother-liquors in
1 When it is required to introduce a liquid into the flame we bend in
the end of a horse-hair platinum wire, a ring of suitable diameter and
hammer the same flat. If we let a drop of the fluid fall into the ring
thus formed a sufficient quantity for the investigation remains hanging
2 Lithium is concentrated so much in the mother-liquors in the man-
ufacture of tartaric acid that we can obtain considerable quantities from
3 Dr. Folwarcznyhas even been able to show with the lithium line Li a
the lithium compounds in the ash of human blood and of muscular
the flame and observe through the telescope, in order to show
at once, that, in many of these saline residues, a rich and
hitherto overlooked lithium source exists. Thus in the process
of preparation, we can follow any loss of lithium in the as-
sociated products and wastes by means of the spectral reaction,
and thus easily seek more efficient methods of production than
those heretofore used. 1
The volatile potassium compounds produce in the flame a
very extended continuous spectrum which only show two
characteristic lines ; the first K a, in the outermost red border-
ing on the ultra red rays falls exactly on the dark line A of the
solar spectrum; the second K $ far in the violet toward the
other end of the spectrum, corresponds likewise to a Fraunhofer's
line. A very weak line, coinciding with the Fraunhofer's line
B, which, however, is only visible with an intense flame, is less
characteristic. The blue line is somewhat weak but is almost as
well suited for detecting potassium as the red line. The position
of both lines, in the neighborhood of the limits of the rays per-
ceptible by the eye, renders the reaction somewhat less sensitive.
In the air of our room it became first visible when we burned
about one gram of chlorate of potassium mixed with milk
sugar. We can, therefore, make clear to the eye in this way
about -nnr^h of a milligram of chlorate of potassium.
Potassium hydrate and all compounds of potassium with
volatile acids, show the reaction without exception. Potassium
silicate and similar non-volatile salts, on the contrary, produce
it only when the potassium is present in large quantities.
With small amounts, the test bead may be melted together
with some carbonate of sodium in order to make the char-
acteristic lines visible. The presence of the sodium does not
prevent the reaction and hardly affects the sensibility. Ortho-
1 We obtained by such an approved method from two jars of mineral
water (about four litres) a mother-water, which gave on evaporation
with sulphuric acid a residue of 1.2 K, half an ounce of carbonate of
lithium of the purity of the commercial, whose cost would be about
140 fl. per pound. A great number of other mother-waters which we
examined showed a like wealth iu lithium compounds.
RADIATION AND ABSORPTION.
clase, sanidine, and adularia may easily be distinguished in
this way from albite, oligoclase, Labradorite, and anorthite.
In order to detect traces of potassium, vaiiishingly small, we
need to heat to a feeble incandescence the silicate, with a large
excess of fluoride of ammonium, in a platinum crucible and in-
troduce the residue into the flame on a platinum wire. In this
way we find that almost every silicate contains potassium.
The lithium salts disturb the reaction but little. Thus, for
example, it is only necessary to hold the ash end of a cigar in
the flame before the slit, in order to produce at once very dis-
tinctly the yellow line of the sodium and the two red ones of
potassium and lithium, the last metal being scarcely ever
absent in tobacco ash.
The spectra of the alkali earths are not so simple as those of
the alkalis. That of strontium is characterized, particularly, by
the absence of green bands. Eight lines of the same are quite re-
markable namely six red, one orange and one blue. The orange
line Sr a which appears close to the sodium line toward the red,
the two red lines Srp, Sr y and finally the blue line Sr 6 are the
most important in their position and intensity. In order to
test the sensibility of the reaction we heated quickly in a plat-
inum dish, over a large flame, an aqueous solution of chloride
of strontium of known concentration until the water was
evaporated and the dish began to glow. The salt then began to
decrepitate into microscopic particles which were thrown into
the air in the form of white smoke. A weighing of the salt
residue in the dish showed that in this way 0.077 grams of
chloride of strontium had passed out into the 77,000 grams'
weight of air of the room in form of a fine dust. After the air
of the room had been thoroughly mixed, by means of an open
umbrella moved rapidly about, the characteristic lines of the
strontium spectrum were very beautifully outlined. We can ac-
cording to this experiment estimate the amount of chloride of
strontium preceptible at T WW fcn f a milligram.
The chlorine and the other haloid compounds of strontium
give the most distinct reaction. Strontium hydrate and carbon-
ate of strontium show them much more feebly; the sulphate
MEM OIKS ON
still less distinctly; the compounds, with the non-volatile
acids, the weakest or not at all. We must therefore introduce
into the flame, first, the bead for testing by itself, and then
again, after previously moistening with hydrochloric acid. If
we assume sulphuric acid in the bead, we must hold it some
moments in the reducing part of the flame before moistening
with hydrochloric acid, in order to transform the sulphate into
the sulphide which is decomposed by hydrochloric acid. To
detect strontium in compounds of silicic, phosphoric, boracic
or other non-volatile acids we proceed best in the following
manner: for fusing with carbonate of sodium a conical spiral
of platinum wire is used instead of a platinum crucible. The
same is made white hot in the flame and dipped into dry fine
pulverized carbonate of sodium which, when possible, contains
enough water so that the necessary quantity of the salt remains
hanging to the same on the first immersion. Fusion can be
effected in this spiral much quicker than in the platinum
crucible, since the mass of the platinum heated is small and
the salt to be fused comes into immediate contact with the
flame. If we transform the fine pulverized substance to be
tested into the glowing fluid soda by means of a small plat-
inum spatula, and maintain it in a glowing state for a few
minutes, we need only to knock the spiral, inverted with its
vertex upward, on the edge of the lamp stand in order to
obtain the contents of the same in the form of a large solidified
bead. Wo then cover the bead with a sheet of writing paper
and press it by means of an elastic knife blade, which we also
use after removing the paper, in order to reduce the mass still
farther to the finest powder. This is collected on the edge of
a plate slightly tilted and carefully covered with hot water
which is allowed to flow backwards and forwards over the sub-
stance, heaped up by gentle tipping of the plate and finally,
the fluid, remaining over the sediment, is decanted. It is easy,
by repeated heating of the plate, to draw off the soluble salt
after several repetitions of this process without stirring up the
sediment and losing an appreciable amount of the same. If
instead of water we use a common salt solution, the operation
may be conducted more quickly and certainly. The residue
contains the strontium as carbonate, of which a few tenths of a
RADIATION AND ABSOBPTION.
milligram, moistened with a little hydrochloric acid on a plat-
inum wire, give a brilliant reaction. In this way, without
platinum crucible, mortar, evaporating dish, and without
funnel and filter, it is possible to carry out, in a few minutes,
all the necessary operations of fusing, powdering, digesting
The reaction of potassium and sodium is not affected by the
presence of strontium. The lithium reaction takes place along
with the three mentioned with perfect distinctness, if the
quantity of lithium is not too small with respect to that of the
strontium. The lithium line Li a then appears as a narrow in-
tensely red and sharply defined band upon the weaker red
background of the broad strontium band Sr p.
The spectrum of calcium can be immediately distinguished at
the first observation from the four spectra already considered
in that a very characteristic and intense line Ca ft is present in
the green. Also a second not less characteristic feature is the
very brilliant orange line Ca a which lies considerably farther
toward the red end of the spectrum than the sodium line Naa
and the orange line of strontium Sr a. By burning a mixture
of calcium chloride, chlorate of potassium and milk sugar we
obtain a smoke whose reaction is approximately of the same
sensibility as that of the fumes from the chloride of strontium
under the same conditions. It follows from an examination
made in this way that T <yo 6 (nnj- of a milligram of calcium chlo-
ride can be detected easily and with absolute certainty. Only
the calcium compounds, volatilized in the flame, show this re-
action, and the more volatile they are the more distinct it is.
Chloride of calcium, iodide of calcium, and bromide of calcium
are best in this respect. Sulphate of calcium gives a spectrum
only after it has become basic but then very brilliantly and
long continued. In the same way the reaction of the carbonate
becomes distinct after the acid has been driven off.
Compounds of calcium with non-volatile acids remain indif-
ferent in the flame, but if they are attacked by hydrochloric
acid, the reaction may be easily obtained in the following way:
we introduce a few milligrams, or perhaps only a few tenths of
a milligram, of the finely pulverized substance on the flat plat-
inum ring, somewhat moistened, into the less heated portion of
the flame until the powder is frittered without being melted.
If we allow a drop of hydrochloric acid to fall on the ring the
greater part of it will remain hanging. If we pass this drop
before the slit of the spectroscope into the hottest part of the
flame it volatilizes without boiling on account of its spheroidal
condition. If during the volatilizing of the drop we look into
the telescope there appears at the instant when the last portion
of the fluid has been evaporated a brilliant calcium spectrum-
which flashes out but for a moment with a small amount, but
continues a longer or a shorter time with considerable quan-
tities of metal.
Only in silicates which are attacked by hydrochloric acid can
the calcium be found in this way; in silicates which are not
attacked by hydrochloric acid the test is best obtained in the
following way: a few milligrams of the substance to be tested
are pulverized as fine as possible and placed on a flat platinum
crucible cover with about a gram of half-dissolved fluoride of
ammonium and the cover held in the flame until it volatilizes
the fluoride of ammonium. We moisten the salt residue re-
maining on the cover with one to two drops of sulphuric acid,
and drive off the excess of the same by gently heating over the
flame. If the residue of the sulphates now remaining on the
cover be scraped together with the finger-nail or a spatula and
about a milligram of the same be introduced into the flame by
means of a wire, we obtain, if K 9 Na and Li are present, the
characteristic reaction of these three bodies simultaneous or
successively. If calcium and strontium be also present their
spectra usually first appear after K, Na and Li have been
vaporized. The reaction of these metals fails with weak con-
tents of calcium and strontium; we obtain it, however, imme-
diately if we introduce the wire for a few moments into the
reducing part of the flame, moisten it with hydrochloric acid,
and bring it again into the flame.
All these tests, as the heating of it alone, or with hydro-
chloric acid, the treatment with ammonium fluoride alone, or
with sulphuric and hydrochloric acid, provide the mineralogist
KADI ATI ON AND ABSORPTION.
and still more the geologist with a series of highly simple tests
for determining many substances occurring in nature even in
the smallest particle, such, for example, as the minerals so
similar to one another, consisting of double silicates, contain-
ing lime, with a certainty which is scarcely attainable with an
abundant supply of material by means of an extended and pro-
tracted analysis. Some examples will illustrate this best.
1. A drop of sea-water evaporated on a platinum wire showed
a strong sodium reaction, and after volatilizing the chloride of
sodium a weak calcium reaction which, by moistening the wire
with hydrochloric acid, became for a moment very brilliant.
If we treat a few decigrams of the residue of sea-water, in the
way described for lithium, with sulphuric acid and alcohol we
easily obtain the reaction of potassium and lithium. The pres-
ence of strontium in sea- water can be observed best in the
boiler crusts of steamships. The filtered hydrochloric acid
solution of the same leaves, on evaporation and solution in the
smallest quantity of alcohol, a dull yellow coloring from the
basic iron salt which is deposited after some days and collected
on a filter and washed with alcohol. The filter burnt on a fine
platinum wire gives, along with the calcium line, a complete
and bright strontium spectrum.
2. Mineral waters often show at once the potassium, sodium,
lithium, calcium, and strontium reactions. For example, if
we introduce a drop of Durkheim or Krauznach mineral water
into the flame we obtained the lines Na a, Li a, Ca a, and Ca /?. If
we use instead of the mineral water a drop of the mother liquid
the same lines appear with great brilliancy. In proportion as
the chloride of sodium and lithium are volatilized and the
chloride of calcium has become more basic, the characteristic
lines of the strontium spectrum gradually develop themselves
and, becoming brighter, finally are seen in all their extent. We
obtain here also, by a mere glance at a single drop vaporized in
the flame, the complete analysis of the mixture of five sub-
stances in a few moments.
3. The ash of a cigar moistened with some HC1 and held in
the flame gives the lines Naa, Ka, Li a, Caa, Cap.
4. Potash glass of a combustion tube gave, both with and
without hydrochloric acid, Na a and K a, and treated with
fluoride of ammonium and sulphuric acid Caa, Cap and traces
of Li a.
5. Orthoclase from Baveno gives either alone or with hydro-
chloric acid only No, a. with traces of K a and Lia\ with fluoride
of ammonium and sulphuric acid the intense line Naa, K a and
somewhat less distant Li a. After volatilizing the constituents
thus observed the bead introduced, into the flame with HCl,
gives only a scarcely distinguishable flash of the lines Caa arid
Cap. The residue remaining on the platinum wire after this
test showed, when moistened with cobalt solution and heated,
the characteristic color of alumina. If we employ the well-
known reaction of silicic acid also it follows from this examina-
tion, made in a few minutes, that the orthoclase from Baveno
contains silicic, alumina, potash with traces of soda, lime and
lithia whilst every trace of baryta and strontia fail.
6. Adularia from the Gotthard conducted itself quite similar
to the orthoclase from Baveno only that the lithium reaction
fulled entirely and the calcium reaction nearly so.
7. Labradorite from St. Paul gives, by itself, only the sodium
line Na a and not the calcium spectrum. But the sample moist-
ened with hydrochloric acid gives the calcium lines CWand
Cap very brilliantly. With the test by means of fluoride of
ammonium we still obtain a weak potassium reaction and very
faint traces of lithium.
8. Labradorite from the Diorite of Corsica comported itself
similarly only that the traces of the lithium reaction were
9. Mosanderite from Brevig and Tscheffkinite from thellmen
mountains gave by itself only the sodium reaction, but the cal-
cium line Caa and Cap when treated with hydrochloric acid.
10. Melinophane from Lamoe gave by itself only Naa but
with hydrochloric acid Caa, Cap and Li a.
11. Scheelite and Sphene gave, on treatment with hydro-
chloric acid, the very brilliant calcium reaction.
12. If small quantities of strontium are present with calcium
we employ the line Sr6 most advantageously to detect the for-
mer. By means of the same it is easy to detect a small content
of strontium in very many sedimentary limestones. Na a,Li a
R a particularly Li a are shown immediately on heating the
KAUIATION AND ABSORPTION.
limestone in the flame. Those minerals, converted into cal-
cium chloride by hydrochloric acid and introduced into the
flame in this form, give the same lines and besides frequently
the line Sr 6 quite distinctly. But this appears only for a short
time and most distinctly whilst it is being developed in the
course of the volatilization in the flame and shortly before the
fading out of the calcium spectrum.
In this way the lines Naa, Li a, Ka,Caa,Cap, Sr 6 were found
in the following limestones :
Silurian limestone 1 from Kugelbad near Prague,
Shell limestone from Rohrbach near Heidelberg,
Lias limestone from Malsch in Baden,
Chalk from England.
The following limestones showed the lines Naa, Lia, Ka,Ca a ,
Cap, without the blue strontium line:
Marble from the granite of Auerbach, 2
Devonian limestone from Gevolstein in the Eifel,
Carboniferous limestone from Planite in Saxony,
Dolimite from Nordhausen in the Hartz,
Jura limestones from the Streitberg in Franconia.
We now see from these few experiments that extended and
careful spectral analysis of the lithium, potassium, sodium,
and strontium content of various limestone formations are of
the greatest geological interest with respect to their order of
formation and their local disposition and may possibly lead to
unexpected conclusions on the nature of the earlier ocean and
sea basins in which the formation of these minerals took place.
The spectrum of barium is the most complicated of the
spectra of the alkalis and alkaline earths. It is distin-
guished at the first glance from those heretofore examined by
1 The lithium line could not be detected with certainty in this class of
minerals, the line Sr <5 on the contrary was very strong.
2 By means of the experiment with alcohol above described enough
nitrate of strontium was obtained from twenty grams of marble to pro-
duce a bright and complete spectrum of strontium. Whether the re-
maining limestones treated in this way show a strontium content we
have not investigated.
the green lines Ba a and Bap, which exceed all the others in
brilliancy, appearing first and disappearing last in weak reac-
tions. Ba y is less distinct but is still always to be treated as a
characteristic line. The relatively great extension of its spec-
trum is the reason why the spectral reaction of the barium com-
pounds is somewhat less delicate than those of the substances
heretofore examined. 0.3 grams of chlorate of barium
burned in onr room with milk sugar gave, after the air had
been thoroughly mixed by moving an open umbrella, the line
Ba a most distinctly, for a long time. We may therefore con-
clude from a calculation made similar to that for sodium, that
the reaction will show, with perfect distinctness, not less than
TTJ ^oth of a milligram.
Chloride, bromide, iodide, and fluoride of barium, the hy-
drated oxide, the sulphate, and the carbonate, give the reac-
tion most markedly and can therefore be determined by
immediate heating in the flame.
Silicates decomposable by hydrochloric acid containing ba-
rium give the reaction, if, as indicated in the case of lime, they
are introduced into the flame with, a drop of hydrochloric acid.
Thus, for example, barytharmotome treated in this way gives
the line Caa Cap along with the lines Baa.Bap.
Compounds of barium with non-volatile acids, which are
indifferent with or without hydrochloric acid in the flame, we
may fuse best, in the way given for strontium, with carbonate of
sodium and then test the carbonate of barium thus obtained. If
in such compounds Ca, Ba and Sr occur together in very unequal
amounts, we dissolve in a drop of sulphuric acid the carbonates
obtained by fusion and extract the salt with alcohol from the
evaporated residue. The residue then contains only barium and
strontium both of which may be easily detected if they do
not occur in too unequal quantities. When it is desired to test
for the smallest traces of Sr or Ba, we transform the residue,
by heating with sal ammoniac, into chlorides, from which the
chloride of strontium can be easily extracted in a sufficiently
concentrated state for detection by means of alcohol. If neither
of the substances to be tested is present in very small quantities
all such methods of separation are quite unnecessary, as the
following experiment shows: a mixture of sodium, potassium,
RADIATION AND ABSORPTION.
lithium, calcium, strontium, and barium chlorides which con-
tained iUh of a milligram of each of these six substances at the
most, was introduced into the flame and observed. At first
the brilliant sodium line Naa appeared on the background of
a weak continuous spectrum. As soon as this began to fade
away, the sharply defined brilliant red line of lithium Li a ap-
peared and on the same side of the sodium line, still farther
away, the faint potassium line Ka whilst the barium lines Baa
and Ba p appeared very distinctly in their characteristic position
and peculiar shade. Whilst the compounds of potassium,
lithium, and barium were slowly volatilized their lines faded
away, or vanished again gradually in succession until, after a
few minutes, the lines Caa Cap and Sra /bV/s Sr% Sr 6 became
visible out of the less and less prominent lines of strontium, as
from a dissolving view, in all their characteristic form, shade
and position, and then faded away and entirely vanished after
a very long time.
The absence of any one or more of these components could
be instantly detected, in the observation, by the absence of the
For those who have become familiar with the individual
spectra by repeated observation, an accurate measurement of
the individual lines is unnecessary; their color, their relative
position, their characteristic definition and shade, the grada-
tion in their brilliancy, are criterions which are quite sufficient
for definite recognition even for the inexperienced. These
characteristics may be compared with the distinguishing fea-
tures which the various precipitates present in their outward
appearance, which we use as a reaction test. Just as the char-
acter of a precipitate determines whether it be gelatinous, pul-
verulent, flocculent, granular or crystalline, so also the spectral
lines indicate their characteristics in the sharpness of their
edges, in the shading off uniformly or irregularly on one or both
sides, or in their broader or narrower appearance, as the case
may be. And just as we use only those precipitates in analysis
which can be produced by the greatest possible dilution, so we
also use in spectrum analysis for this purpose only those lines
which require for their production the smallest amount of the
substance and only a moderately high temperature. In such
characteristics therefore the two methods are quite similar.
On the contrary spectrum analysis furnishes, in the color phe-
nomena used in the reaction, a property which gives it unlimited
advantage over every other method of analysis. Most of the
precipitates which are used for the detection of substances are
white and only a few colored. Further the tint of the latter is
not very constant and considerably differentiated according to
the greater or less condensed state of the precipitate. Often
the smallest mixture of a foreign substance is sufficient to oblit-
erate completely a characteristic color. Small differences of
color of the precipitate can therefore be no longer used as a
chemical test. In spectrum analysis, on the contrary, the colored
bands remain undisturbed by such foreign influences and are
undisturbed by the presence of other bodies. The positions
which they have in the spectrum determine a chemical charac-
teristic which is of as unalterable and fundamental a nature as
the atomic weight of the substance, and therefore, permits us
to determine it with an almost astronomical exactness. What,
however, gives to the spectral analytical method a peculiar im-
portance, is the fact that it almost infinitely exceeds the limits
to which chemical analysis of matter has heretofore reached.
It predicts for us the most valuable conclusions on the distribu-
tion and arrangement of geological substances in their forma-
tion. Already the few investigations, which this memoir
contains, lead to the unexpected conclusion that not only
potassium and sodium but also lithium and strontium must be
counted among the substances of the earth most widely scat-
tered, though only in minute quantities.
Spectrum analysis will also play a not less important part in
the discoveries of elements not yet detected. For if there are
substances which are so sparsely scattered in nature that the
methods of analysis heretofore used in observing and separating
them fail, we may hope to detect and determine many of them,
by the simple examination of their spectra in flames, which
would escape the ordinary method of chemical analysis. That
there are actually such elements heretofore unknown we have
.already had an opportunity of showing. We believe that we
shall be able yet to declare with absolute certainty, supported
RADIATION AND ABSORPTION.
by the unquestioned results of spectral analytical methods that
besides potassium, sodium and lithium, there is still a fourth
metal belonging to the alkali group which will give quite as
characteristic a spectrum as lithium a metal which shows,
with our spectral apparatus, only two lines, a weak blue line,
which almost coincides with the strontium line Srd and another
blue line, which lies only a little farther toward the violet end
of the spectrum, rivaling in intensity and distinctness the lith-
On the one hand spectrum analysis offers, as we believe we
have already shown, a means of wonderful simplicity for de-
tecting the slightest traces of certain elements in terrestrial
substances, and on the other, it opens up to chemical investi-
gation a field heretofore completely closed, which extends far
beyond the limit of the earth even to our solar system itself.
Since, by the analytical method under discussion, it is sufficient
simply to see the gas in an incandescent state in order to make
an analysis, it at once follows that the same is also applicable to
the atmosphere of the sun and the brighter fixed stars. A modi-
fication with respect to the light which the nucleus of these
heavenly bodies radiate must be introduced here. In a memoir
"On the Relation between the Emission and the Absorption of
Bodies for Heat and Light " 1 one of us has proven, by theo-
retical considerations, that the spectrum of an incandescent gas
is reversed, that is, that the bright lines are transformed into
dark ones when a source of light of sufficient intensity,
which gives a continuous spectrum, is placed behind the same.
From this we may conclude that the sun's spectrum, with its
dark lines, is nothing else than the reversal of the spectrum
which the atmosphere of the sun itself would show. Hence the
chemical analysis of the sun's atmosphere requires only the
examination of those substances which, when brought into a
flame, produce bright lines which coincide with the dark lines
of the solar spectrum.
In the article mentioned, the following examples are given
as experimental proof of the theoretically deduced law referred
1 Kirchhoff, Pog. Ann. Vol. CIX p. 275. See previous memoir.
The bright red line in the spectr-um of a flame in which a
bead of chloride of lithium is introduced is changed into a
black line when we allow full sunlight to pass through the
If we substitute for the bead of lithium one of sodium chlo-
ride, the dark double line D (which coincides with the bright
sodium line) shows itself in the sun's spectrum with unusual
The dark double line D appears in the spectrum of the Drum-
mond's light if we pass its rays through the flame of aqueous
alcohol, into which we have introduced chloride of sodium. 1
It will not be without interest to obtain still further confir-
mations of this remarkable theoretical law. We may arrive at
this by the investigation which will now be described.
We made a thick platinum wire incandescent in a flame and
by means of an electric current brought it nearly to its melting
point. The wire gave a brilliant spectrum without any trace
of bright or dark lines. If a flame of very aqueous alcohol in
which common salt was dissolved were introduced between the
wire and the slit of the apparatus, the dark line D showed it-
self with great distinctness.
We can produce the dark line D in the spectrum of a platinum
wire which has been made incandescent by a flame if we merely
hold before it a test tube into which some sodium amalgam has
been introduced, and then heat it to boiling. This investiga-
tion is important, on this account, in that it shows that far
1 In the March number of the Philosophical Magazine for 1860
Stokes calls attention to the fact that Foucault had made already an
observation in 1849 which is similar to that mentioned above. In the
examination of the electric arc between two carbon points he observed
(1, Institut 1849, p. 45) that in the spectrum the same bright lines were
present in the position of the double line D of the solar spectrum, and
that the dark line D of the arc is intensified, or produced, if we allow
the rays of the sun or one of the incandescent points to pass through it
and then resolve them in the spectrum. The observation mentioned
in the text gives the explanation of this interesting phenomena already
observed by Foucault eleven years before and shows that the same is not
influenced by the peculiarity of the electric light, which is still, from
many points of view, so enigmatical, but arises from a sodium compound
which is contained in the carbon and is transformed by the current into
RADIATION AND ABSORPTION.
below the point of incandescence of sodium vapor, its absorbent
effect is exercised exactly in the same parts of the spectrum
as with the highest temperatures which we are able to produce
and at which that of the solar atmosphere exists.
We have been able to reverse the bright lines of the spectra
of K, Sr, Ca, Ba by the employment of sunlight and mixtures
of the chlorates of these metals with milk sugar. Before the
slit of the apparatus a small iron trough is placed; into this the
mixture was introduced, and the full sunlight passed along
the trough to the slit and the mixture ignited on one side by an
incandescent wire. The telescope was set with the intersection
of its cross hairs, which were mounted at an acute angle with
one another, on the bright line of the flame spectrum, the
reversal of which was to be tested; the observer concentrated
his attention on this point in order to judge whether at the
moment of ignition a dark line was visible, passing through
the intersection of the cross hairs. In this way it was quite
easy with the proper proportion of the mixture, to be burnt, to
establish the reversal of the lines Ba a and Ba ft and the line
K /3. The last of these coincided with one of the most distinct
lines of the solar system, although not indicated by Fraunhofer;
this line appeared much more distinctly at the moment of ig-
nition of the potash salt than otherwise. In order to observe
the reversal of the bright lines of the strontium spectrum in the
way described, the chlorate of strontium must be dried in the
most careful manner; a slight trace of moisture causes the sun's
rays to be weakened and produces the positive spectrum of
strontium on account of the flame becoming filled with salt
particles which have been spattered about by the ignition.
"We have limited ourselves in this memoir to the investiga-
tion of the spectra of the metals of the alkalis and alkaline
earths, and these only in so far as was necessary for the analysis
of terrestrial matter. We reserve for ourselves the further
extension of these investigations which are desirable in connec-
tion with the analysis of terrestrial substances and the analysis
of the atmospheres of the stars.
Heidelberg, April, 1860.
MEMOIRS ON RADIATION AND ABSORPTION.
ROBERT WILHELM BUNSEN was born in Gottingen March 15,
1811. He received his doctor's degree in 1830 and became
private-decent in 1833 in that University. In 1836 he became
Professor of Chemistry in the Polytechnic School at Cassel and
in 1838 accepted a similar position in the University of Mar-
burg. In 1851 he went to Breslau and the following year to
Heidelberg, where he remained until his death. Both as a
teacher and as an investigator, he was one of the most eminent
of his generation, making many important contributions to
both Physics and Chemistry. His spectroscope, photometer,
calorimeter, gas burner, filter pump, battery, etc., on the one
hand, and his early contributions to organic chemistry, the
methods of gas analysis, photochemical action, etc., on the
other, illustrate the versatility of his genius. His work in con-
nection with his colleague, Kirchhoff, resulted in one of the
most brillant achievements of the century, the application of
the spectroscope to the analysis of terrestrial substances,
which revealed at once several new elements and showed the
common constitution of all bodies in the stellar system. His
final contribution was made in 1887 after an illustrious scientific
career of nearly sixty years. During his last years he was a
familiar figure on the streets of Heidelberg, in which city he
died Aug. 15, 1899.
Brief list of publications of historical importance.
NEWTON. [Radiation.] Phil. Trans, p. 827. 1701
PICTET. Essai sur le Feu. 1791
PREVOST. Recherches sur la Chaleur, Jonr. de Phys. 1792
PREVOST. Du Calorique Rayonnant, 8 Geneva. 1809
PREVOST. Sur la Transmission du Calorique, etc., Jour.
de Phys. de Chim. 1811
HERSCHEL, W. [Radiations beyond spectrum.] Phil.
LESLIE, J. Inquiry into the Nature, etc., of Heat.
RUMFORD. Memoires snr la Chaleur. Paris. 1804
DELAROCHE. Obser. sur la Calorique Rayonnant, Journ.
de Phys. de Chim. 1812
FOURIER. Sur la Chaleur Rayonnant Journ. de Phys.
de Chim. 1817
DULONG ET PETIT. [Law of Cooling.] Ann. de Chim,
et de Phys. 1818
HERSCHEL, J. [Spectra of Colored flames.] Ed in. Phil.
FRAUNHOFER. [Spectra of flames] Gilbert's Ann.
1823, Harper's Series II. 1898
TALBOT. [Spectra of flames.] Brewster's Jour, of Sci.
MELLONI. Sur la transmission de la chaleur Rayonnant,
etc., Ann. de Chim. et de Phys. 1833-37-39
MELLOXI. La Thermochrose ou la Coloration Calori-
que, Naples. 1850
DE LA PROVOSTAYE ET DESAINS. [Law of Cooling.]
Ann. de chim. et de Phys.
MEMOIRS ON RADIATION AND ABSORPTION.
DE LA PROVOSTAYE ET DESAINS. [Relation of Absorp-
tion and Emission.] Ann. de Chim. et de Phys. 1853
DRAPER, J. [Law of Draper.] Phil. Mag. 1847
DRAPER, J. [Max, Solar Energy.] Phil. Mag. 1857
FOUCAULT. [Reversal of D lines.] Soc. Philomatiqne 1849
STOKES. [Note on Foucault and KirchhofFs Obs.]
Phil. Mag. March. 1860
STEFAN. [Stefan's Law.] Wien. Akad. Ber. 1879
LANGLEY. Researches on Solar Heat. Washington. 1884
BOLTZMANN. [Deduction of Stefan's Law.] Wied.
Ann. XXII. 1884
WIEDEMANN, E. [Luminescence of Vapors.] Wied.
;, ; ( 1879
Ann. < 1889
RAYLEIGH. [Radiation and Molecular Motions.] Phil.
WEBER, H. F. [Weber's Law A Jftf = const.] Berl. Akad.
WIEN. [Laws of Displacement, Emission, etc.] Wied.
Ann. j 1894
PLANCK. [Law of Emission.] Ber. Deut. Phys. GeselL
Absorption and Radiation, Relation of .... 40
Assumption made in establishing Kirchhoff's law . . 76
Alum, Observation on . . 27
Barium, Observations on 119
Bath, Description of 25
Black bodies, Proof of law of radiation for . . 78
Bunsen, Biography of 126
Calcium, Observations on 115
Caloric, Nature of 17
" Clausins' " law ',. . . 94
Cold, Reflection of 7
Conduction and Radiation, Relation of .... 49
Diathermancy, Table of 37
" General 69
Distance, Law of 9
Draper's law 95
Dulong and Petit's law ........ 67
Emissive and Absorptive power 75
Equilibrium of heat, Meaning of the 4
Fluids, Radiant and non-radiant ..... 12
Foucault, Observations of . ' . . . . . . . 124
Glass, Observations on . . . . . 26-29-12
Heat, Conduction of ...'.. . 12
Absolute and relative equilibrium of ... 7
" Nature of . . 4
Helmholtz, Law of . ; . ... . . . 88
High temperatures, Radiation at 59
Kirchhoff, Biography of 97
Lampblack, Use of 26
Le Luc, Ideas of / . . . 3
Le Sage, Theory of . . ..,.,. ;. ,. . 4-17
Leslie, Observations of . 26
Lithium, on ...... r . 109
Mercury, Eadiations from . ... . . . 61
Mica, Observations on . . , . . . . . . 27-29-32
Mutual Radiations of black bodies . | , . . 83
Pictet, Experiments of . .... .' . ', . . 8
Potassium, Observations on . . . . . . 42
Prevost, Biography of 20
Principles and Conclusions, Resume of .... 18
Quality of heat radiated, Experiments on . . . . 33-34
Radiation and absorption, Relation of .... 40
" from polished surfaces and lampblack ... 26
" and refractive power, Connection between . . 42
*' and conduction, Relation of 49
" for different thicknesses, Law of . . . . 29-31
Radiant Heat, Second Series 53
Radiating Substances, Table of 28
Ratio between Emissive and absorptive power of ajl bodies 78
Refractive power on radiation, Influence of ... 42
Reflective " ' 4< " "... 42
Reversal of Spectra . 123
Rock-salt, Observations on 28-30-33
" Quality of heat radiated from .... 54
Selenite, Observations on 27
Sodium, Observations on 107
Spectral Observations 101
Spectra produced by spark . 106
Stewart, Biography of .... .... 72
Strontium, Observations 011 113
Swan, Observations of 107
Temperature and Radiation, Law connecting ... 64
Temperature of different flames 105
Theory of exchanges, Extension of 23
Thermo-multiplier, Description of 24
Thick and thin Plates, Radiation from . 33-34
Tourmaline, Radiation and Absorption of .... 95
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